Hi Bgcpost,
The first thing you might want to look into is the residency conditions, I am a citizen so I am not familiar with with all of the options for obtaining residency, but I have heard a lot of talk on expat groups about new regulations that are going to make it more difficult to border hop.
To answer some of your questions:
1/ I wish to be a self entrepreneur in Peru, is it better to open a shop, a guest house or an online shop for someone with a small budget? - I think this would largely depend on you and your budget, for example if you are not really a people person, then running a guest house may not be the best option, likewise is you do not have a background in sales and marketing, then an on-line shop may not be a good choice. As someone that is currently running a bed and breakfast, I can tell you that the tourism industry here in Peru is growing and could be a good industry to get into.
2/ What kind of business is booming in Peru these past years? - Tourism and Mining
3/ What's the best thing to sell online these days? - Cant help with this one, sorry
4/ Is it a good choice to open a business or some are not available for foreigners? - Sorry, no answer for this on either.
5/ Is it a safe country? - I think so, I have been living here for over 5 years now and while there are areas to avoid, in general I think that Peru is safe.
6/ How cheap is the real estate? - This really depends on where you are looking, sale price wise an apartment in Lima could run you between $60,000 and over $200,000 in smaller towns you could get a nice home for under $100,000, sometimes furnished.
7/ Is it better to open a business from scratch or to buy one for sale? - This is another one that I think really depends on you, starting from scratch can be a cheaper option, but can also take a lot more work between marketing and building a good reputation. Buying a business allows you to take advantage of an established reputation and clientele, but will cost you more as well. We actually purchased our property and started our B&B from scratch, I can tell you that it was a lot of work to get it going, but we have enjoyed it and are now planning on switching directions and are selling the B&B.
Another good source of information would be to check out some of the expat groups on Facebook, Living in Lima – Expat Support is a good one.
Hope this helps,
Lyle