Body Posture & Finger Placement

I started playing classical-style with the guitar on the left leg. I think I should switch but it's hard. Help!
If you started playing with a ‘classical' posture then your hands will be used to playing that way and making the switch will feel difficult, but not for long. As with most things, when you try something new it usually takes a little getting used to, and this is no exception. You should find that after a few weeks of playing it will feel better and you'll probably have a hard time going back to the old way.

That said, some people simply prefer playing with the classical posture, and that is fine too.

How does one go about holding top-heavy guitars?
Top heavy guitars (where the headstock is heavy and the neck pulls toward the ground) can be a pain. My Gibson Les Paul Gold Top is really top heavy and the only thing I have found to help is to use a strap and stand up. I don't practise a lot with Les Pauls for this reason, but I know other people who love the feel of them, so it's just a preference I guess.

When I place all four fingers on the fretboard, my index finger tilts inward towards/away from my other fingers. Is this bad?
Everybody's hands are a little different, don't worry about it! There are some guitar freaks out there that seem to have ‘guitar-shaped' hands with perfectly even finger lengths, that seem to be able to stretch to grab any chord with ease, but that's not the case for most players. I have a tiny little finger, but I don't find many chord grips I can't play... I've seen dudes with HUGE ‘farmer's fingers' that can still play intricate jazz grips and little kids playing amazingly difficult stretches with tiny hands... it just takes practice!

My hand touches the neck just next to the high E string. Is this a really bad habit?
As a beginner, yes, you should avoid this. You will probably find that your hand will often mute the thin E string, and also hinder your chord change speed. Later on, you might find that it's O.K. to have the hand gripping there, but you are better off not learning that way. This is one of those things that will change as you develop your guitar playing, but you can't start like that.

You may also find that your hand is supporting the neck, which is bad as well.