First off, I am using my Elf Assassin to describe how I did it. I also started from scratch and did not give her any starting items, what she has, she earned it through blood and sweat( mostly blood).
Secondly, Traps and Pickpocketing are very useful for a solo Assassin, Traps in particular.
Thirdly... have patience... ...
Fourthly, make sure you get the Boots of Speed as soon as possible, my Assassin got hers around level 12.
Fifthly, do not ditch potions. You are soloing, and until you level up sufficiently, potions will make up for your limitations. Oil of Speed is especially important here until you get your Boots of Speed.
DO NOT UNDERESTIMATE what potions can do for you, I used potions for Nalia's Keep, Tradesmeet, Copper Coronet, etc... ...
Sixthly, never get complacent.
Seventhly, never use Potions of Invisibility freely, they are going to be your wildcard if your stealth attempt fails. Remember this.
Firkraag: what lvl rogue and items are needed to beat em solo?
Traps, if for some reason this is not to your liking, use the Tuigan Bow( 3 attacks per round). Do not use normal, +1/2/3 arrows, use Arrows of Ice, Biting, Acid, etc... ...
Obviously do not use Arrows of Fire... ... 
For protection, drink Potions of Fire Resistance, read scrolls of Fire Protection. Just make sure that your Fire Resistance is 100% and above for the entire duration of the fight.
If you do not possess the Boots of Speed yet( and I highly recommend that you do so first)... drink an Oil of Speed potion.
Drink a Potion of Clarity to avoid the effects of Firkragg's Chaos spell.
When you are all buffed up and ready to go, use hit and run tactics on Firkragg. If you are an Assassin like me, make full use of your Poison Weapon ability.
Shadow dragon: same question
More or less the same answer as the Firkragg one, but slightly more difficult because of the level drain. Remember that the Amulet of Power grants Immunity to level drain, so you might want to wait until you level up enough to get the Use Any Item ability before tackling the Shadow Dragon.
planar sphere: same, I don't see how one can beat the cold room, fire room, the gov district mage there with his buddy, and then Lavok who death touches. The damned halflings are somewhat of a pain.
Why not? Backstab my friend... backstab... ...
Again, speed will play an important factor here, and now, stealth. Engage stealth before entering any room, if an enemy mage casts True Sight, run away and wait until the spell duration runs out. You may want to play sniper too and use the Tuigan Bow to shoot once, run away and stealth, shoot again, run away and stealth, etc... ...
For Tolgerias and his buddy, you are going to need to do a bit of legwork( aka Boots of Speed or Oil of Speed potion).
Remember, they still cannot see you even after you open the door. So go stealth and enter the room. When they cast True Sight, retreat out of sight and stealth again. Repeat until they run out of True Sights. Proceed to backstab Tolgeria's buddy and run away out of sight and stealth again. If you are lucky, she will succumb to the first backstab, otherwise, start using the sniping tactic because they will have activated their stoneskins by now.
Lavok is easy... after you open the door to his room, engage stealth and backstab him, IMMEDIATELY after backstabbing him, run out of sight and stealth. Wait for his spell protections to run out until he is left with stoneskins only. Use the Staff of Fire you should have obtained from the Fire Room and summon a Fire Elemental to engage him. It is okay if the Fire Elemental loses, just summon another one until all his stoneskins are gone, then backstab him again. If you wish, you can also assist the Fire Elemental by shooting elemental arrows with your Tuigan Bow.
With regards to the Halflings, I used sniping tactics. Slow? Yes. Tedious? Yes. Efficient? Hell, yes.
Nalia's keep where there is the Yuan ti mage and 2-3 trolls: even the last named troll was tough ( so level and items needed to beat em?) I'll skip the burrowers since they can be lured to the back.
Yawn, this is going to sound boring, but I used the sniping tactic again, with one difference, I used a Light Crossbow of Speed and Bolts of Biting. As we are dealing with Trolls here, we want to limit their rate of regeneration, and I doubt most people would have enough traps( and set traps skill points) to make this reasonably easy, unless for some bizzare reason they chose to do this area late in the game.
I used several Oil of Speed potions and used the conveniently circular dungeon( where you are supposed to put the dog stew) to lead Torgal on a merry-go-round of poison hell. When I finished with Torgal, I led his two Troll bodyguards in the same manner.
Remember, you can isolate Torgal from his bodyguards.
Vampires: what's a rogue got to help em against these things and what level to tackle em on?
Try to avoid Vampires at all costs in the beginning. Walk the streets of Amn during the day, rest if it is nighttime. Try to get Daystar as soon as possible, and your Use Any Item ability so that you can wear the Amulet of Power and use the Mace of Disruption. You can fight maybe one Vampire fight a day, using the Daystar. Backstabbing hit and runs works very well here if it comes down to that( remember to drink an Oil of Speed potion if you do not have Boots of Speed).
Golems: heh....can I say iron golems backed up with other golems hasted is a beat down. A rogue without boots is gonna have a tough fight.
Oil of Speed and Traps.
the prison: one area you want to visit to get your boots of speed to help for other areas... yet, npcs there can see invis AND there is an area with GREATER WOLFWEREs. ( even the first fight when you get in is tough for a solo person, you got a rogue backstabber and mages on your heels)
If you are fighting Greater Werewolves, then you are unneccessarily taking the hard path. Follow the slaves' advice and go east( aka right) from the first encounter to eventually fight the Demon and obtain the orb from him.
Potions are the order of the day here. Drink every single damn potion that you can drink and have not drunk yet, because this is going to be the turning point of your solo Thief's career. Make use of your Bhaalspawn powers too, if applicable.
Your first target is going to be the enemy thief. He will backstab you, you will grit your teeth in pain, drink a healing potion and hit him as fast as possible. Grab his Boots of Speed and heal up if necessary.
Take out your Tuigan Bow and start aiming at the enemy swordman. Ignore the enemy archers, drink healing potions to nullify the damage being dealt to you. Ignore the enemy mages, their flame strikes will do nothing to you if you have 100% Fire Resistance. After you take out the swordman, take out the archers, and finally the mages.
I succeeded on my fifth try.
Lichs: same..use a scroll and then? run out to waste npc magix?
Use a scroll of Protection from Undead... ...
Gaxx: pro undead scroll again? on both forms? what of imprisonment and summoned creatures. Here, I can picture running out of harm's way on the first lich to have it's pit fiend help. As for weapons, use the staff of Rynn of sling of everard. This is one of the areas you can drop stuff off before hand and pick your tools. NOt all places are like this.
Wait until you can use the Mace of Disruption. Set several Traps for the first form, use a scroll of Protection from Undead for the second form, and proceed to beat out a tune on Kangaxx's head with your Mace.