My dos colones, ask an ex-pat that lives there rather than listen to anything that pseudo-experts like me say. Its not that guys like me won't know at all what we're talking about. Its that the ex-pats will know much better. Personally, the longest I've stayed in SJ has been 1 month. I stayed at the Linda Vista apartments, but I've at least checked out personally the other 2 places you mentioned. So here are my own answers to your questions.
1) You'll pay for location. In general prices will be cheaper the further out from the city center you go but prices will be higher the nicer the neighborhood you stay in. Rather than rehash this subject which has been written on many times, why don't you check out what I and others posted in these threads:
http://www.costaricaticas.com/phpBB2/viewtopic.php?p=40195
http://www.costaricaticas.com/phpBB2/viewtopic.php?p=52720
I will add a few comments. Of the places you listed, I've stayed at or at least checked out personally all of them and I'd have to say that the Sudamer is IMHO the best deal in terms of quality of apartment and proximity to the Gulch for the price, however it is in the scuzziest neaighborhood of the three and it runs at the top of your price range. Much nicer places can be found for much less if you're willing to stay somewhere you'll need to take a bus into town.
You want to be within walking distance to the P4P but that is going to greatly limit you and you will pay in more than one way for that "benefit". Your choices will be greatly restricted, the cost for equivalent quality will be much greater than the deals you get elsewhere and if you opt for the P4P everyday (particularly the BM) instead of trying to develop regular pros that will come to you or, even better, non-pro contacts, over a few month you'll pay much more extra than the cost of the apartment (plus it will probably grow a little old). On this last point, I would add that that is one of the big advantages of living in CR over a period of time. I'm not saying you should live out in Escazu like VB, LVSteve, Easy and others but I wouldn't be afraid to live in a place where you had to take a bus into town (or cab back later at night). It will probably be a much nicer place for the money.
2) Problems taking chicas back to apartments? Its your place and you can do whatever you want. I doubt you would have any problems at any apartment you'd rent or at least not in the way that you'd think. Just keep in mid that there are some advantages to having to check in your chica. at least someone else checks her ID, if you fail to do it. They also record it or even hold on to it while she is with you and if they hold on to it usually won't give it back unless you give the green light. Also few if any apartments include a room safe. If you bring a chica back and she slips you a mickey or goes through your things while you are in the bathroom or, in the case of TLN's, are asleep, then she can't just slip away. If the front desk guy has her ID, she won't get it back without your say so. And even if she has her ID or is able to get it back, her name has been recorded and you're more likely to be able to track her down if it turns out she ripped you off. Those protections probably won't apply if you stay in an apartment.
3) I can't say on the outage issue, but its never been an issue when I've been done there and doesn't sound like it would be much of an issue based on what others have said.
4) Automercado and Mas x Menos are very much like grocery stores in the states, albeit with a lot of brandnames you're probably not familiar with. Pali's are certainly much cheaper, but spartan is a bit of an understatement. They're unlike anything back in the states unless you've been into a mercado in some immigrant barrio. No racks or fancy coolers, just rows of stacked boxes of groceries and some run down equipment for meats and perishables along the sides. Usually, you can find one or the other of these within walking distance or at least a short busride of where you live. The pulperias you're probably already familiar with are like 3rd world convenience stores. There's usually one just a short walk away but limited selection and more expensive than their larger alternatives. The Mercado is a colorful and very cheap place to shop, but there's only one. There's also Mercado Borbon, a couple of blocks to the north of that, and it actually is probably a little better for food and fresh produce. But you'll probably need a cab or bus to get to either of these. If you don't mind traveling to stock up on your weekly staples, Price-mart is another place to consider, particularly if you live further out. It is more like a Super-WalMart, that you might already be familiar and comfortable with, much fancier than the Mercado but still cheap if you don't mind buying in bulk.
5) Differences between long term stays vs. short vacations? As I said the longest I've been there at one time has been a month but I did notice some trends. You may have already noticed that one of the chica interview questions, aside from where you stay, is how long you in Costa Rica. They try to size you up for whether you are a one shot deal to be pumped for as much cash as they can right away or whether you are someone they can work over time. I think that gives you a lot more power. If they do a really good job they know you'll be back for more and keep coming back for quite a while. Not only will they be willing to work harder but they will be more willing to cut a deal if they know it will lead to regular and reliable contributions to their livelihood. And that is just with the pro's in the P4P market. Really working at scoring a non-pro is a practical waste of time for the week at a time guys, unless perhaps they travel to CR every month, but even then that puts a crimp on their action. As a resident you can work a non-pro. If you don't score right away, you have other places to go, but given time and patience eventually something will pay off for you.
One last thing, unless you hang only with CRT'ers and other gringos, you will begin to pick up more Spanish. I suggest you take advantage of your time in CR and sign up for a language course. Unless you're already fluent, even if you think you already speak some, you'll pick up a lot more with a formal class. While you could also take informal lessons from the BM putas, where you learned might wind up reflected in how you speak (sort of like going to the hood and listening to ebonics to learn english). And you can't spend all your time phucking and mongering anyway, so lessons are a worthwhile alternative activity to keep you busy and out of trouble.