I played through Ultima 4 until the very end and really liked it. The only exception was the last dungeon. It really annoyed me when I made my way to the bottom floor just to realize I had forgotten to pick up the black stone. So I had to go out and then go trough the whole dungeon again. I made it to the end but now I could not continue to do the last "ritual" because I had not all followers with me. I really did not want to have them as the game is quite slow in battles so its faster to just have one character. But now I understood I would have to do that part all over again just because I was forced to recruit all members!

At this point I really wanted to finish the game, because it had taken quite a bit of time to come this far. I really did not want to have to go back to every city again to recruit everyone and then do that dungeon again just because of this. So I ended up watching the last 5 minutes of the game on youtube.
After playing through the whole game that of course soured the experience a bit to just have to do that at the end, but it still was better then the alternative to waste all that time doing all that again.

Now I think this was very annoying and I wonder if there is something similar in the other Ultima games? Are there these really annoying and slow last parts where you have to redo so much stuff if you "forget" something? Also I have heard that you can import your character from the previous game. Because I did not finish it with my character will I be missing out if I start playing Ultima 5?

In Ultima 5, there's a specific item that you need to bring with you. If you don't... well, it's effectively game over. Ultima 6 doesn't have the same long final dungeon arrangement so it isn't a problem there.

As for importing: doing so gives you several advantages at the outset but a fresh start will eventually get you to the same point. (Starting via import gives you the 'Avatar' class immediately and you'll probably have much higher Str/Dex/Int at the outset.)

You don't need a full party in the rest of the series, I think you could technically solo the rest of the series (but don't take my word for it). There will stil be requirements to have certain items in your posession though. As for ultima IV, you can recruit all the companions then just let the ones you don't like die and revive them before the last shire. I'm not sure if you even need to revive them, but after coming all the way down I didn't want to risk being throw out again.

You can import your character into Ultima V for an experience boost, which is a nice feature. I don't think you need to have beaten the game or become a partial avatar. If importing is broken for you (as it was for me) look in the sticky thread for the link to a fixing program that can patch up your save file.

AFAIK the only real advantage to importing your Ultima IV character into V is that it saves you some redundant grinding at the start, since you start at a higher level than you would have done otherwise (though your stats get nerfed rather significantly). And there's so little difference in importing from V to VI that part of me has to wonder why Origin even bothered with the feature in the first place, although it does mean you can start the quest without going through the tedious Questions of Virtue first.

Unfortunately, there are no plot or gameplay changes if you import your character versus starting from scratch, so far as I know.

There is an Ultima 4-6 save editor. I had to use it once in U5 when I got stuck in a room, ran out of keys, and saved by mistake. Maybe you could get that and just edit the file so you have all party members.

The mechanics are as follows:

Your stats from Ultima IV will be halved - but that's alright, since the maximum of 50 in U4 was lowered to 30 in U5, so if you had max stats in U4, you'll have nearly-max stats in U5, and will have no trouble (between Shrine quests and gaining levels) getting them up quite high.
You Experience will be reduced to one-tenth, which can give you a starting level of four or five (depending on whether or not you had more than 8,000 EXP last game), compared with a starting level of three if you just create a new character.

The game, however, assumes that you've already beaten Ultima IV and picks up the story from there, regardless. You ARE the Avatar, which is how the game treats you throughout.

Basically, it allows you to skip over the exploration and grinding that you had to do to learn your way around Britania in U4, since it assumes you know where things are and how to fight and such. That's about it. It's the equivalent of "Thanks for buying our other products!" bonus, in the long run, and it doesn't really affect the challenge in the mid- or endgame, only at the start.