Hi WW, and welcome.
Firstly, with a few exceptions (which don't include the Lakes) you cannot legally 'wild camp' in England, without the permission of the landowner. Since you are going to find it difficult to find the landowner of a particular spot in the lakes, technically you can't camp.
However the reality is different, and generally if you're camping at high level, and leave no sign of your presence the next day, no-one is particularly interested. In fact once when I was passing Angle Tarn (near High Street in the Lakes), I rather got the impression it was a bona fide campsite there were so many tents.
Safety? Now there's a question. If you're worried about the local yobs, most of them wouldn't climb 10 feet let alone 2,000. There is of course the occasional rabid sheep, and rampant bunny, but if the landowner did catch you, the worst he would probably do is order you off. However if you are concerned about safety, as an alternative there are a lot of Youth Hostels in the Lakes where you would be safe, including some very remote ones such as Black Sail.
Now tents, that's another question. There's been a thread on wild camping on this forum with plenty of hints, tips and usage reports. Take a look there.
With regard to sleeping bags, I personally have an old version of the Vango Ultralite 1100, which is warm enough for snow conditions (I've been there), but a down bag will be lighter and pack smaller. I wouldn't really recommend anything lower than a 3 season, unless you intend camping in July and only in July or want to buy several bags. I have considered upgrading to a down bag myself, but have discarded the idea on the basis that the loss of weight/pack size is not huge, whereas the cost is. However if you've decided you need a new bag certainly consider down if your budget will go to it.
There's also been a number of posts on this forum regarding gear in general. Take a look there and if there's any other queries just ask. In fact I agree with you that asking here is probably the best way to get info, especially on gear. The walking magazine reviews are quite good for getting an idea of a product's features, but it is doubtful that they are tested over extended periods while this forum's members have probably used their stuff for years.
S.