Ok, I will attempt to answer your question, but just remember, this is what I do. Things tend to be a little different for other people. I always say this...what works for ME may not work for YOU. But, with how I do things, it works pretty well.
Depending on what you are using to germinate with will help you know when you need to water. If you use a starter soil, its a little harder. You'll have better germination than pellets, but its easy for a beginner to screw something up. Trust me, this is my first year this year, and I started with a starter soil. I was over-watering EVERY time. Killed my seedlings. Had to re-sow a whole new set. A solid month wasted there. IF you use a starter soil, here is what I do....I wait until right when the plants look like they are about to start wilting, or will even let them actually wilt a little, then water. I had started by looking at the soil, and when it LOOKED dry, I watered. BIG no-no! Just because the surface LOOKS dry, that doesnt mean its dry underneath. The bottom is always the last to dry. (Dries out from top to bottom.) Your roots are going to reach for the moisture, so if you keep the bottom more moist than the top most of the time, then the roots will be inclined to grow downward. Which will also help your plants grow.
If you use peat pellets, they are easier to know when to water. (When they're dry and light colored, and FEELING, its time to water.) BUT, there are 2 downsides to that. Pellets sometimes dont germinate as well as starter soil. Some people have better luck than others do with pellet germination, so most will either love pellets, or hate pellets. I personally love pellets. But, I buy the starter soil as well. Its all personaly preference. Second down side is is that you have to water them more often than you would soil. I would water my pellets every day to a day-and-a-half.
Again, these are just MY opinions and what has worked for ME.
As far as fertilizing goes, I also started fertilizing my 1st set of plants when they were babies, and they died. I dunno if it was just the over-watering, or if it was fertilizing them, or both. I suspect BOTH. Either way, on my 2nd set of plants, I didnt start fertilizing until I transferred them to their 3" pots. Which, coincidentally, I do when the seedlings get their 3rd to 4th set of true leaves. Again, others do it differently. This is just what I do. When you DO start fertilizing, start with a weak fert. Water it down. Its better to UNDER-fertilize than to OVER-fertlize.
As far as your spray bottle question goes, doesnt really matter. It'll be a lot harder if you spray than if you just pour the water. When you use pellets, or with soil actually, bottom water. If using soil, most of the little "black trays" have holes in the bottom. Just get you a bowl of water, set the container in the water, and as soon as you see the top of the soil get darker, remove it and go to the next one. Same with pellets. Set the pellet in the bowl, and when the top gets dark, remove it. Just the way I did it.....lol
Hope this helps ya!