Thanks for your reply.
50 lbs of live rock is about one third to one half of what is generally recommended. This is the biological filtration of your system, so you can't cut back on this amount too much. You can use dry rock if you are willing to wait a few months for it to become populated with bacteria and in effect become live rock.
A 10 gal sump is extremely small for a 100 gal tank. I surprised you could get this to work at all. How do you have the sump set up, and what kind of return pump are you using? While I don't think this is a direct cause of your problems, this may be something you'll need to work on for long term success.
While you don't absolutely need a skimmer, I would consider this to be so highly desirable that I wouldn't set up a large tank with out one. Be careful in you shopping here. There are a lot of low end junk skimmers on the market, and you only want to buy this piece of gear once. Additional note, you seem interested in large predator fish, some of which produce a lot of waste. A good skimmer really helps with these.
I forgot to ask this before. What species of trigger did you get? Some of them are really nasty and can't be kept with other fish at all.
SG is specific gravity. It's measured with a hydrometer or refractometer. Typical reading for a reef system is about 1.025 - 1.026. Fish only systems are sometimes kept at a lower level, about 1.021 - 1.022, but I prefer using the same level as a reef system.
At this time, don't worry too much about the algae issues.
Since you mention using a dechloranator, I assume you used tap water to mix your salt. This could also be the source of your problems. Tap water today has a lot of garbage in it. It can only be used if you live in an area that has very light quality water. Most reef keepers today use RO/DI water, and get that either from their LFS (Local Fish Store) or get their own RO/DI unit. Since you have a larger tank, I highly recommend you get an RO/DI unit so you have a source of high quality water.
As you can see, getting all this gear can get expensive fast. Don't panic and feel you need to get it all at once. However, when you do buy equipment, always get top quality. This doesn't mean most expensive. It does mean getting something that will last for years, and you will not need to replace it after a few months or a year.
If your just a little handy with your hands, you can make a lot of your own equipment. This can save you a bundle.