I didn't find where to ask them in existing topics so I have to create one.

I just started another Dawnguard playthrough (having finished the Dawnguard side) and this time I accepted the cursed gift with my lv7 redguard.

I have 2 problems:

The first one is I have a disease that drains my stamina in addition to the 60 damage from lv4 stage vampire. So I have 15 stamina . Are not vampires immune to diseases? I know the resistances and weaknesses have been halved with Dawnguard but the description still says 100% disease resistance.

The other problem is that when I switch to Vampire Lord, I have to first go to ground, then go up again to have the possibility to cast the standard spells/attacks. I have seen some videos and that doesn't happen there.

You SHOULD be 100% disease immune as a vampire...
Not sure about your other problem, you might need to phrase that better but I'll answer according to how I understand the question.
Everyone has to switch from spells to attacks in Vampire Lord form, if they don't have to then they're using a mod which I've never heard of and I search for mods almost daily.

So I had a weird bug with that disease problem . Maybe I catched it in VL form and this form doesn't have the same resistances? It's a problem we don't have access to the menu of effects in this form. Maybe I should try a console command "player.getav diseaseresist" or something like that. I'll try that next time I play this character....

For the 2nd problem, when I switch to VL form my hands are empty (no spells selected) while it seems the default blue (animate dead) and red (drain life) must be selected. I can select manually the left hand via the favorites menu but not the right hand. If I do down, touch the floor to go beast mode and then go up again to go magic mode I then have the right spells selected by default and can change the left one as I wish.

This (your second) problem happened to me too. If you're sneaking when you transform, you start on the ground. BUT, sometimes this "sticks" like if you hit CAPS LOCK at certain points and the function gets reversed. Right now, I'm stuck with on the ground as I change, no biggie though, just hit a key.

The right spell is always the drain life spell, as far as I know it cannot be changed.

Have you tested your vampire lord during the night time? Perhaps I misread, but you do realise that your health, stamina and magicka are reduced during daylight hours, as well as the lack of hp/magicka/stamina regeneration?

If I misunderstood, I apologize in advance.

I have to hit the ctrl key twice since I'm already flying, just no spell in hands. If I try to cast with right hand it doesn't do anything. Yes I have 60 reduction in stats, that has been taken into account but that doesn't apply here, it happens all the time and in dungeons too. I will try to seat in a chair if it can solve the problem.

Well, maybe that's the price to pay to have a super powerfull character . Sometimes it's not even funny how strong he is even on master.

Sounds like a made up story, I thought you had to be level 10 or above to activate the Dawnguard DLC.

Hum, I thought that the stats stay the same, except that you get a penalty to regeneration instead? I may be completely wrong too, since I have only ever been a Werewolf (LOVE) and a Dawnguard... (so far).

You can start the Dawnguard storyline at level 1 if you want. If you need more convincing look at this let's play : http://www.youtube.com/watch?v=ZC1bLdpZSj8&feature=channel&list=UL

At least pre dawnguard if you are past stage 1, possibly even at stage 1 vampirism, you get stats lowered in the sunlight. I just remember my stamina being 75 at some point in the sun as a vampire.