Do hosts usually bill monthly, or charge you for the whole year/2year contract up front?

Shared hosting services are billed on annual basis, especially if they cost less than $10 month. But you can also find some web hosts which offer monthly billing for shared plans. Those however cost $10 - $15 per month.

I prefer annual payment once you know your hosting provider quite well, besides there are some services my host Hqhost.net provides only on condition of annual payment in advance.

Sorry for the ambiguous answer, but it depends on the individual hosting company. As mentioned by fcolor, some very cheap plans may only have an annual payment option, but I have seen hosts that will bill you monthly for even $5 plans.

In general though, you may get a bit of a discount if you go with an annual or 2 year plan. I personally don't know if I'd go for 2 years up front, considering the somewhat fickle nature of this industry where companies either change hands or go out of business all the time.

What kind of services from HQhost.net are provided only on the condition of annoual payment? Do you think it's fair enough with respect to those customers who need hosting say only for 6-10 months?

Hqhost.net site says that it's only VPN and proxy services that you should pay for on annual schedule.

To the OP, I think all depends on the web hosting company itself. Some companies offers to pay for 3 or 6 or 12 months and you may economize some money. For example, A2hosting.com offers the following pricing:
Monthly Fee $4.95
3 Month Price $4.75
6 Month Price $4.45
12 Month Price $3.95
24 Month Price $3.45.
As you see paying for more time, you may have cheaper services.

The discount of 30% is really impressive, coupled with their 20percentoff coupon this might give you a good deal and decrease your price twice, anybody here using a2hosting.com services? How are they?

Do you mean a coupon code 20PERCENTOFF that guarantees 20% discount on A2hosting.com on all their services? If yes, it sounds great.

Not only www.a2hosting.com offers so nice discount on their services but many other companies as well. Say www.webhostingbuzz.com offers their clients to pay for 12 Months $4.95/Month and for 24 Months $3.95/Month. And this company provides also coupon on their services whb108 which gives out 50% discount.