So, as stated above, the file size is going to vary for each MLS, as they are all independent of each other. And "MLS" is short for "Multiple Listing Service", and there can be more than one operating in a given area, such as Phoenix AZ, where I think there is something like 6-8 "MLS" associations. The Phoenix MLS's all have a data share agreement, which is nice, as the agent only has to load to their association, and it gets broadcast to all of them. If you need more specific info about file size, you should contact the local association, and speak the the MLS staff there. FLEXMLS is a common MLS service provider, they are based out of ND, and the staff at the local association can contact them (or whoever they use) about file size requirements. It's kinda convoluted, but hey, welcome to real estate!
I use either the native photo editing software in my Macbook Pro or Adobe Lightroom CC for my editing tools. Adobe is far more capable than the native photo app, but you have to pay for it.
As far as loading info to the MLS site, using the agents login is probably the best/easiest, but as an agent myself, I don't give out my login info to anyone, vendor or otherwise. When I do a photo shoot for clients, I load the images to a DropBox file after editing, and share the link to the file with the agent and let them load the files to the MLS themselves. They can place them in the order they want, and they need to do some of the work themselves, too, for the amount of commision received is more than enough to spend 15-20 minutes organizing photos on THEIR listing.
Hope this helps!