Industry is a catch-all term for all the industrial activities within EVE:
Industry is vitally important to the EVE economy and activity, as without industrial-minded players building the ships and modules and ammunition required for PvE and PvP combat, combat-minded players could not function. Virtually none of these items are seeded on the market; almost everything in EVE is player-built (you can identify NPC sell orders on the market by their >300 day duration).
A quick look at some Industry alts can be found on the Industry Skill Plans page. For a more in depth look at the skills for each section of Industry check out their respective pages.
It's a lot of work for what you get. You can run a casual production business on the side and make a bit, but not much. Most producers do it as their whole job and it takes quite a bit of capital to do. I DO however recommend running a production business on the side that is related to what you do. Run missions? Put up buy orders for mission loot you know is undervalued. Sell ammo that you know is used in missions. Put up sell orders for items you know your agent demands. Put up buy orders for items you know your loyalty point store offers. If you really like to PvP in a ship and you find that it's constantly out of stock or overpriced then build some just for shits.
Not at all. More popular items have bigger profit margins because they tend to run out in the hubs which keeps the price less sticky up (you clear the market every once in a while and you can cheat downward pressure on prices). Build things that are used commonly in missions and PvP. Don't trust the fittings on the eve-o forums, trust the fittings you know are used by you and other TEST people. Your best source of evidence on what to build comes from what you wish was more available on the market.
Ships are often sold nearly at cost in empire, but the popular ones are still the best source of raw profit. You will need Advanced Industry V, good trade skills, and good standings to make it worth building ships to sell in empire. Also consider the System Cost Index when finding a place to build in empire. In TEST space, minerals are fairly easy to come by, either by buying locally from miners, or by importing compressed ore.
It can be good to avoid really cheap modules because with a lot of the popular cheap stuff guys will run massive piles and dump that inventory on the market all at once.
T2 modules are always in high demand. Everybody needs Damage Control IIs, and things like Heat Sink IIs or guns often get purchased in larger stacks than other modules.
Generally stuff that is harder to build has higher margins. That includes items with long build times, items that use a lot of Megacyte/Zydrine relative to other stuff (in part also because people don't realize that by placing buy orders early in the week and babysitting them to keep them competitive you can get much lower cost zyd/mega), and items that use a lot of Isogen because that's usually a bitch to buy.
As far as T2 modules go, your margin depends chiefly on your supply chain. If you have a good source of a particular T2 part, that can boost your profits nicely. If you have perfect invention skills, that also will help. If you can spot a “natural market” and seed it before other people catch on, that can allow you to have much higher prices.
A lot. Buying minerals for full scale battleship production is a full time job, I only recommend it if you can keep an eye on eve while at work. Mineral orders need to be babysat and constantly updated to keep them competitive otherwise they aren't sold to. Sell orders also need a lot of attention sometimes. Building stuff in 0.0 markets or building stuff you know to be neglected by the market in a mission-running hub are easy though. There is a middle ground, but you'll tie up more capital placing orders you don't babysit. For guys like Halliburton it's all about inventory turnover. Build a Raven, sell a Raven, use that ISK to buy minerals, use those minerals to build a Raven. Rinse. Repeat. If you can do that 3 times a week you're making 3 times as much profit as if you only do it 1 time a week, using the exact same amount of capital.
There are still some items you can make in Nullsec for a profit by buying and importing compressed Highsec ore and refining it. You will need very good refine skills for this.
The skills Scientific Networking and Supply Chain Management allow you to remotely start research and production jobs. However, everything for the research or production job must be in the same place. You cannot have a Blueprint in another system and minerals in another and start a production job where the minerals are. The same goes for invention and other research.
The one exception is that you can have a Blueprint in a corp hanger and still be able to remotely start a production job in a POS as long as the minerals are in the POS.
When you install any industrial job - manufacturing or science - you need to pay an installation cost. This installation cost is calculated per system, and is dynamic, being based on how many other people have been using that system for manufacturing over the last 28 days (measured in job-hours, not # of jobs or # of people).
The system cost index is calculated by the number of system-job-hours, divided by total-universe-job-hours, and then square rooted for better numbers. This value (measured as a percentage, generally in the 0.01% to 5% range) is then multiplied by the job base value, which is:
NPC stations have a 10% tax on top of this final value.
You can find out the system cost index for nearby systems by using the Facilities tab of the Industry window. Each activity at a certain facility will have a red bar at the bottom of the icon, indicating relatively how expensive it is to install a job there. Mouseover will show you what can be built there, and a more detailed indication of the system cost index (see image to right).
You can also find system indexes by using this CREST endpoint.
Choosing a system with a low system cost index is important, but it must be weighed against the possible impact of having to move your materials and/or products to market. Picking a very low cost system at some distance from the market hubs may seem attractive at first glance, but your transport costs for that further distance will be increased instead.