I literally just returned from DW with my 13 month old boy and can answer many of these questions!!
Couple of questions for the 'baby.'
1. Can he literally ride on my lap on certain rides like IASM or PotC? IASW definitely yes, my little guy was obsessed with this ride. It is so mellow, he was in the front row standing and holding on to the front of the boat and having a ball. The carrier is fine too, it depended on his mood whether I had him in the carrier or just sittign on the lap. He also went on dumbo, haunted mansion, carousel (sat on a horse and my husband stood to the side - also a favorite), Anna and Elsa, peter pan, toy story (I worried this was too jerky but he was with my husband and wasn't crying so I guess not). Of course he also LOVED anything remotely splash pad. sometimes the safety bar comes down and I had to shift to the side a little when he was in the carrier and I was also wearing my backpack. We didn't go on POTC this time, I did think there was a slight drop that he wouldn't have liked but he didn't mind the drops on A&E at all.
What about the safari at AK? We didn't go to AK, I would not have taken him on this only because I remember it being very uncomfortable and jerky.
How do rides work with a little one? Can I wear him in a baby carrier on the ride ( we will have a stroller but I didn't know if I should bring the carrier too)? see above, definitely bring the carrier if he likes it. My guy napped in it a couple of times and it was good to keep him contained in lines, rides, etc.
2. Can I take him to a mothering station and let him nap with me in a rocking chair there for half an hour or is it only for nursing? Don't know, I thought about this too. I also thought about taking him to the contemporary and finding some comfy chairs to nap in, as I read online this was an option. But, it turned out we never needed it - he was either wide away and stimulated or he napped in the carrier. Once he napped in the stroller, but he is not a big stroller napper. We were only there 2 days.
3 Will characters interact with or hold the baby? No, right? That would be dangerous, right? ( You can see parts of me think it would be adorable for Cinderella to hold the little man... But goofy not so much?)
Definitely interact, I didn't ask anyone to hold him as I thought they probably wouldn't want to or weren't allowed, but pretty much every character my daughter met also spoke to him and interacted with him. I am sure they would have been happy to have him in the photos too, we just didn't want to mess with it. But they were very good with him. I'm sure there are ways you can have him in the photos without them holding him.
4 I assume any food place that has hot water will fill a bottle for us, yes? How about heat infant food?
I would assume they would do this, but my son was eating table food so I didn't try it out.
Any other tips for traveling to the world with baby boy? TIA
I used garden grocer and had milk, baby food pouches, baby snacks, diapers and wipes delivered to the hotel (they were there waiting for us when we arrived), so that I didn't have to lug all that stuff along. My guy is very active and he was restricted all day so we looked for opportunities to let him have a "walk-a-bout" - the splash pad at MK, the dumbo play area, fountains at epcot, splash pad at the hotel (it was hot), the baby play area under the bridge near splash mountain, and the open area in front of Hollywood and vine at HS. He was otherwise trapped in the stroller and the carrier for so much of the day. He loved the rides! He would literally cry when they stopped. Use ride share - that is such a great benefit and my daughter got to ride snow white and splash mountain twice!
We considered going back to the hotel for a nap like we did when my daughter was 3, but we ended up letting him nap on the go and were back to the hotel for a fairly early bedtime (8-ish). We brought a decent sized stroller that would lay flat and had good shade and I was glad we did that because it was so sunny and an umbrella stroller would not have cut it for this trip. I can't think of anything else off the top of my head but please feel free to ask any questions! Disney is the perfect family friendly place for a 1 year old so do not be nervous, you will be amazed at the accommodations.