I'm a screen printer by trade, flat sheet though, and I've never had anything to do with glass or formed shape printing and not to shoot down nebben but...
I believe the ink they use is a 2 pot ink, and possibly kilned on as well. 2 pot ink is hella nasty, as soon as its mixed it starts to dry and will dry into your screen. As soon as your finished printing you'll wanna clean the hell out of your screen otherwise it's rendered useless.
Buy a pre-stretched screen opposed to stretching it yourself - it's easier and will save you a lot of dramas, you want a nice even tension across your screen, should only cost $20 or so for the prestretched frame, try and get an angled mesh at 45 or 22 degrees, it's a bit more expensive but gives a crisper image.
I think you'll need nylon instead of polyester as nylon stretches around the bottle shape better.
You'll also need to make sure you get the correct mesh count (threads per inch) and thread thickness. Too high of a mesh count means the openings are too small so you won't get a nice ink deposit and you'll have ink drying in your screen, too low - you'll get a crappy image and too high of an ink deposit.
You'll need to get the correct squeegee rubber - again soft rubber - too much ink, hard rubber - not enough, a fabric rubber would be too soft I would think.
Don't brush your emulsion on, use your squeegee to sort of 'scrape' it on, you want to push it through the threads but not too much pressure. Try and get a nice even layer, go from top to bottom of the screen with your squeegee in one even motion without stopping until you get to the top. Generally, and depending on mesh count, you'll want to coat the substrate side first and then turn the screen around do the squeegee side twice. There's a few vids on youtube of coating screens.
Like said above, stick to one colour, you'll have a hell of a time getting register on a bottle and especially on home set up. You could try two colours but make sure they're far enough apart that any misalignment isn't very noticable. Also in saying that I think to get any decent bright colours you'll have to lay down a white and print your colour on top, depends what the inks are like and the colours your going for and substrate colour.
Remember you can only print one colour at a time so either buy multiple screens or wash off and recoat for the second colour.
I wouldn't tape up pinholes, they can start to leak after a few impressions. You're better off using a paint brush and spotting them with emulsion, then dry it and re-expose it so that emulsion used for spotting hardens.
And just you know, it's not painting with paint, you're printing with ink ;-)
45deg squeegee angle is too much I reckon, 75ish is usually the norm, but it's all about experimentation. You really need to have a play with angles and pressures and all that to see what works.
You'll want a little offcontact distance between your substrate and screen mesh, again something of trial and error.
I wouldn't go over the image more than once, you'll be asking for a blurry/bleeding image, and I don't think your rig would be accurate enough to be able to lay down the second hit in the exact same place.
If your image is bleeding out around the underside of the screen you're using too much pressure and/or don't have enough emulsion over the mesh threads - the idea here is that the emulsion should create a gasket seal to the substrate. Printing is all about kiss impressions so be gentle with it.
Ink up your screen, take a light stroke over the image while the screen is lifted up, this is to fill the screen with ink (and also helps stop your ink drying in), then place your screen down and go over it again - a little more pressure than last time but only just enough to make it touch the substrate. You're not really trying to 'push' the ink through the mesh, more like a 'rolling transfer' of the image.
The ink will be solvent based too, not water based, so you'll need to have some turps or reccomended solvent handy.
You'll really need to pull out the yellow pages and look for a local industry-focused screen printing supply shop - I don't think art and craft stores will be much help. Go down and talk to those guys and ask for some advice. Printers are generally pissheads so a few beers won't go amiss
I'd love to see your rig and your final product.
Good luck.