First time brew soon; a few quick questions

Unless your beer will sit on the yeast for a couple months or more, I wouldn't worry. Secondaries are usually not necessary, and, especially for a first batch, add an unnecessary complication.

 

No, don't sweat that. If you were to lose a good amount into the boil, though, you would want to strain them out. Grains shouldn't go in above about 168F or you risk some harsh, tannic flavors.

 

Strain them out? Yes.
Worry? No.

 

Give the yeast plenty of time to clean up. I usually shoot for 3 weeks til bottling day. I check the gravity a few days before bottling and then real quick before bottling. If you are dry hopping I would definitely wait 2 weeks and take a gravity reading while you have it open. If it is stable it is ready to go. The first brew you are so anxious to taste but allowing the yeast to clean up will reward you.

Any site will have caps. The shipping on a little item may get harsh. If you have a local shop that is the best bet unless you have more you want. And who doesn't have more stuff they want to buy. Amazon may work for you too.

 

Like @bluehende ... rest two full weeks in the primary then add dry hops to the primary and rest another week before to bottling. More better to wait than bottle too soon.

Some folks draw multiple samples to see when it's reached its FG but in the end all you might gain is packaging a day or three sooner. IMO ... why bother.

 

After a couple of weeks your beer may be ready to bottle. However, you should take a gravity reading a few days ahead of your hoped-for bottling date, and then again on your bottling date. These two readings should be the same, but if the second reading is significantly lower, then you need to take a third reading a few days or so later because that second reading says that your beer is still fermenting and should not be bottled yet. You can also compare your readings to the expected final gravity that came with your recipe. That is also an indicator whether your beer is done.

 

For many beers and beer styles; 3-4 weeks is the ideal window for the yeast to do all of their partying and clean up.
Don't really worry about getting technical and racking to secondary (yet.)
If you want to do the additional straining for particles and such, get a mesh hop sack, or order a racking cane filter and put it over your racking cane when you are ready to bottle.
On another note; I found in working with buckets that I like to rack to the bottling bucket a day before I bottle so I can give the yeast a jolt with the priming sugar and to allow the priming sugar a chance to thoroughly mix in. I've gotten fully carbed beer that way in a matter of days.

 

You MUST take every precaution to ensure that no penguins are harmed. It's not just the right thing to do, it's the law! Penguins and penguin habitat protection are amongst the biggest, most pressing issues facing homebrewers today.

this message brought to you by Big Penguin Shill

(as a side note, you could think about things like sanitation, fermentation temperature, yeast pitching temperature, have a written procedure etc, but those would obviously be secondary to your penguin preservation efforts)