[RPG] Can a familiar travel any distance

You cannot end the effect early, but this should not prevent the wizard from speaking to the people around him.

The wording of the effect is very clear: until the beginning of your next turn. It is also important to note that the familiar does not move until its own turn, not during the wizard's, thus necessitating the full duration.

The wizard is deaf, but not dumb. Nothing about the spell or the defended condition prevents speech, although volume control would be impaired. The wizard could relay information to his companions, although he could not hear questions from them.

Now, there is one more point to consider. Can a character communicate during another character's turn? The chapter on combat, in the section entitled "Other activity on your turn," it says that you can communicate as you are able "as you take your turn." This does imply that you cannot communicate during any other turn. Since the familiar doesn't move until its own turn, the wizard will not be able to speak until the effect ends anyways. If the familiar is already in position before the wizard's turn in which he activates the effect, the wizard can describe what he sees at that time, although may speak more loudly or quietly than he intends from being deaf.

Yes. The only restrictions on a warlock's familiar are those presented in Pact of the Chain and in find familiar itself.

Pact of the Chain tells us that the warlock can even cast find familiar, and that they have some additional forms available to them. (PHB p.107)

Find familiar has no restrictions on the alignment of caster or of familiar. (PHB p.240)

N.B. You're not actually summoning a quasit, in your example. You're summoning a familiar, a spirit, that takes the form of a quasit. But the familiar does have "the statistics of the chosen form" which does include alignment (MM pp.6-11). So, by RAW, your familiar does inherit the alignment of its form.

However... "the alignment specified in a monster's stat block is the default. Feel free to depart from it..." (MM. p.7) So while most quasits are CE--and perhaps all quasits tend to CE?--this is definitely a situation where things are left to be worked out on a case-by-case basis.