How many slots do the new research labs in Eve Online have

Yes, it can definitely be done.

You can buy a 30-day PLEX from the in-game market. PLEX are purchased by other players and listed on the market, which means it's affected by the normal supply and demand that affects nearly every marketable item in EVE. So, the price can go up or down over time. You can check the price of items on the market out of game using online tools, such as Eve Central. Eve Central has the market listing for 30 day PLEX here. If you know what you're doing and have the time, you should be able to fund the PLEX you need with in-game currency.

The only difficulty is in that "know what you're doing" part. Instead of actively playing (which can easily take more than a couple hours a week) you need to utilize all the methods of generating income while offline. Research Agents, Planetary Infrastructure, and The Market are the three biggies. You'll need a while to set all that up, and now that EVE Online has Alpha clones, which are free to play, you have the ability to set up most of the skills you need without subscribing. And you'll have to play a bit more than a couple hours a week to get it up and running, too.

Warning: Some mission grinding to increase faction standing will likely be required. Some necessary skills are not accessible as an Alpha clone and will require subscribing.

On the whole though, I'd say that if your "addiction" only means a couple hours a week, then you haven't got any addiction to speak of. 8)

This does bring up the valid question of how to use those three methods to generate ISK.

How to make ISK while online

• Kill NPCs (preferably in 0.0 space with low true-sec) - you'll be able to make between 20M and 30M a "tick" (20 minutes of flying anomalies)
• Do high-sec missions

How to make ISK while offline

1. Use the market to generate income
   1. Use the market to buy things you need and sell things you don't need. This will teach you the basics of how it works: buy orders and sell orders. Also explore the 'details' section where you can see the volume traded per day and the low and high prices that day. Notice the systems that the majority of buy and sell orders are based in, this is the 'regional market hub'.
   2. Find items that have a high trade volume in your region and that you can post a low buy order for. Post a buy order.
   3. Collect your purchases, transport them to the market hub (or anywhere that you can get a good price for them) and post a sell order for them. People will pay a good price if you're selling the item they want at the station they want.
2. Develop Planetary Infrastructure (will require some skills that are accessible only by buying game time)
   1. Use the market to find a planetary resource that sells well in your area.
   2. Find a planet that you can produce that item on, drop a Command Center on it, build extractors (and factories if necessary) to produce that item.
   3. Keep those extractors running constantly. Set them to run for as long as it will be till you can set them again.
   4. Post low buy orders for all the planetary resources you're producing on your planet as detailed in 1-2. This is a good alternate source of resources if you can't produce enough raw material to satisfy your factories (and really, who can?)
   5. Transport resources you've purchased cheaply to the planet, take away resources you've created on the planet. Sell those resources as detailed in 1-3.
3. Get Research Agents (will require some skills that are accessible only by buying game time)
   1. Find corporations in your area that have R&D agents. Get the best R&D agents you can. Research the Datacore items they can produce for you, look on the market for which one is the most profitable in your area, start the research. Drop a pile of Tritanium in the station where the agent is.
   2. Run missions for those corporations to raise your standings with them. Note: The missions that Research Agents give once a day count towards the 16 you need to get a storyline mission. Try to get the storyline mission from an agent in the R&D corp.
   3. Once the higher standings you've achieved give you access to higher quality R&D agents, stop the research with the old and inferior agent and start up a new research project with the new and improved agent.
   4. Collect datacores every now and then, sell them as detailed in 1-3.

Note that market ability is the key skill here, all other methods are merely ways of cheaply generating things that you can then sell on the market for a nice profit. Market ability only takes a couple hours to train on your character, but your personal skills at it will develop for years and years.

Short of building and maintaining a POS, you can use this search tool to find all stations in the EVE universe with particular characteristics.

You will probably need to use in-game tools to identify stations with spare slots, but this should at least make finding the stations a bit easier.