1

You can find one when you get there. It all depends on what you prefer. Should you plan to spend your first night in Lima and not at the airport, it may be advisable to book a hostel in advance just for that first night. Normally people travel without sleeping bags. Some do if they intend to trek. Sometimes one may find a small sleeping bag convenient in cold nights.

2

You don't need to book in advance for Cusco, although if you are arriving late at night you may prefer to do so rather than traipse around in the dark looking for somewhere to stay.
You don't need a sleeping bag if you're staying in hostels. You will need one if you do a trek that involves camping, but you can hire sleeping bags in Cusco.

3

No need to bring a sleeping bag if you are not planning on doing any tenting- and even then, as the poster above pointed out, you can rent a bag for a few days while you are on trek.

Perhaps a part of the problem lies in the word hostel. When North Americans or Europeans think of the term they are imagiining young backpackers' accommodation as in YHA (Youth Hostel Association). In South America you see the word *hostal*- with an "a" and not an "e". Hostals offer private rooms and many have ensuite bathrooms included. They do seem usually to be on the budget side of the scale.

I stayed at the Hostal Marani in Cusco (great reasonably-priced place!) and it was definitely not a youth hostel even if there were backpackers all around! To complicate matters, when I just googled Hostal Marani, what should pop up but hostel marani! Check this article for a traveller who has worked herself into a state of total indignation over the South American use of the term "hostal"-

http://www.southamericaliving.com/is-a-hostal-really-a-hostel-in-south-america/

Book at least your first night's accommodation before you arrive. It is easy enough to do on-line.

4

It's low season now in Cusco so you don't really need to book something in advance. If you have plenty of time no worries but if time is short I would recommend you to reserve a place to crash.
Don't forget Cusco is at 3.400 MASL which isn't really funny if you have to look for a place to stay with all your gear.
Another plus if you have a place booked in advance is they will pick you up from the airport, at least that's what they do where I always stay in Cusco.