I've been slowly struggling through the game with a diverse group, yet I see that some are doing it with a single character. I looks as though most of the time, it's a mage who travels alone. My question is: do solo players start from scratch or progress to a somewhat higher level, and then start over using the "improved" character by somehow importing him/her into a newly started game?

If I manage to get through the game the first time, I may try the solo approach next.

it can be done either way but generally you're going to be so powerful anyway it doesn't make sense not to start from scratch. My solo was started at the normal starting level. He's in tob now, having fun dealing with dead magic and wild magic zones.

Almost all soloers start from scratch. It looks hard, and in some ways it is. In others, it's actually easier. If it's your first time soloing, here's what you can expect:

on one hand,
-fights will be a lot tougher, especially at the beginning
-you'll lack some abilities, for example can't detect traps or can't heal/buff yourself, can't hold your own in a toe-to-toe fight, or whatever, depending on your class
-you won't have the interesting NPC dialogues nor quests
-you'll have no backup when a hold spell or similar is cast at you, basically you're a sitting duck in such cases
-you'll always be outnumbered
-you can carry far fewer items

on the other,
-You only have to worry about one character. this makes it far easier to pick on characters one at a time, and to control the actions
-Your character levels up much faster, as XP is not split between different characters. This means the abilities you do have will soon be more powerful than they would be at a similar stage in the game with a party
-you'll not have to buy as many items, meaning you'll have lots more gold to spare. Instead of buying six sets of medicore equipment, you can have one better set.
-All the potions and gear you find are yours alone! All of it! No need to share, so that's all the best equipment for you and noone in the party will be worse off for you keeping it. Those healing potions are all yours too, no need to share. Watch out though as frequent use may damage the liver [img]tongue.gif[/img]

The inability to disarm traps and open locks doesn't have to be a disadvantage, as wizards can open locks with certain spells, and using protective spells can survive the damage those traps deal. Fighters can often shrug off the damage due to their high hitpoints and can smash the locks. And having played the game several times before soloing means you'll know where to watch out for traps in the first place.
The reduced inventory space is not too much of a bother as long as you know what is important and what not. Since you can't use all the items for yourself, you'll be selling plenty. As wise soloers take on one quest at a time, you will not be laden with quest objects. And then there are bags to increase the availiable space.

After a slightly more difficult start, you'll get access to all the good stuff and can really start doing some damage. Of course, since the game was designed mostly to be played with a group of six, the challenge will remain as a soloer would have to be six times as powerful as a character in a party to be equally effective in a contest of raw power. Which is why mages are often more interesting than fighters, as they offer all kinds of spells to bring advantages in battle if you know how to use them.
Tactics are important, and knowing your enemy helps. I compared it to an action movie once before and I think it's not that bad a comparison. Lone hero takes out all manner of baddies one or two at a time, sometimes with stealth, other times with fireworks, until the final confrontation with the badguy. Although actionheroes have the luck their opponents can't seem to hit them unless it's called for by the script...

Instead of jumping directly into soloing (which is great fun) you might wish to try using a reduced party of say three. You get most of the benefits of soloing but it’s not quite so lonely. Controlling three party members is infinitely easier and it allows you to have a variety of skills and talents available to you.

My last time through I started as a ranger and dueled to a cleric at level 9. I took only Yoshimo with me, out of habit more than anything else and did only a minimal number of quests, the circus tent, the slavers and De’Arnise keep before setting off to spellhold. Any spare money I had was spent on scrolls for Imoen and once she was back with me this allowed her to gain some much needed experience. In the Underdark I did only the minimum to complete the quest and pick up Solaufein. After he joined we completed the Underdark quests, returned to the surface and went to work on all those leftover quests from chapter 2. Shortly after arriving in ToB my PC maxed out as a Cleric at level 40 and there was nothing that could stand up to the three of us.