Hello Melanie and welcome to this great forum! Thank you for your great post!
It sound like your child is developing fast and he sound like a amiable boy!
I tried to answer to your questions the best I could. Hopefully you find the answers useful to you.
-How important is it to put words into categories? I have not categorized things, other than that they are familiar objects to him.
It is easiest for the toddler to start reading from objects he already knows. I wouldn't stress too much in categorizing them if it doesn't come naturally.
Understanding categories are expected from children probably only when they turn three or four years old. I think it is very important to introduce them (birds, actions, plants,..) as soon as possible to help the child to build abstract thinking. This might sound weird but I see this like I am providing my son a library card system to memorize for organizing data in his mind with easier already thought logic
-Is the number of new words I'm introducing acceptable?
I haven't read Glenn Doman's "How to teach your baby to read" but in "How smart is your baby" Doman proposes showing 5 flashcard * 5 sets on each session and on fifth day retiring one card from each set. This would result on introducing 5 new cards on each session. You should do what suites your family the best.
-Is the length of slideshow acceptable? (about 40-50 slides)
Yes, this sounds reasonable. We do about 100 slides on best days on 20 on other days. You should always stop before your toddler loosing his focus on it.
-What is the longest recommended interval time between slides?
Use one second at most on one slide. The idea is to use "the right side" of the brain for reading the words which works exactly like photographic memory on adults. The idea is NOT to read the information with consciously thinking ( which would be left side of the brain instead of the right side we are now trying to use). This ability to use mainly the right side is lost when the child turns three or four.
-How do I introduce uppercase letters? Plurals?
In Little Reader Plurals were introduced some where around day 80. Regarding upper case letters, I am not certain what is the best way. We are just showing all words in low case, names in upper case and sentences starting with upper case.
-How will I know if he is processing the words? I tried going through the first slideshow slowly after 5 days, asking him what some of the words were (the ones he already uses verbally). He didn't give me any indication that he recognized them.
You shouldn't test your boy at all.
You should just trust that he is getting it. Testing will result you being frustrated and tense and it takes the focus out of you two bonding and having fun. Your boy will show his knowledge in two to six months by showing his expertise by change when he is ready. If your boy is able to sit still when you flash the cards, I would take it as a indication he is getting it.
When should I start to try teaching him spelling? After he learns all the letters?
I would start learning spelling immediately. Little Reader is a great product introducing spelling. You can try it for free.
Then I decided to make it more personal and created a slideshow with photos of things that are very familiar to him (including things that he already uses as spoken words).
Sounds like you are a perfect mother!
He started to get tired of the first slideshow on the 5th day.
Our baby also got bored with some often shown slides so I started showing them half as many times after that to keep the slides fresh and new to my boy.
-Any other recommendations?
Have fun and enjoy this great time in both of your lives!
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This is probably a phase he is going through. 
