I have live in Norway (a few months shy of a year) and, before that, lived for almost a year in Denmark. I have visited Sweden, though at that time I only had mostly forgotten school Swedish at my disposal. I can currently have reasonable discussions with people using any of these languages, though I occasionally have to ask what a strange word ...
You are correct in both your statement. "Mannen har en katt. Hans katt äter sin mat." does indeed mean that the cat is eating the cat's food. To refrase it so that the cat would eat the mans food using possesive poronouns you can, as you say, use "Katten äter hans mat" or "Hans katt äter hans mat" instead.
Swedish grammar is reasonably regular; for böjning of nouns you can find information online, for example at https://www.worddive.com/grammar/sv/svensk-grammatik/2-bojning-av-substantiv/
The key principle is that you add "-et" to the end of the word; if it already has ä vowel at the end, then ä transforms into e. Vowels are not doubled. The profession-type ...
You can check out this webpage that offers books in easy Swedish sorted into three levels of difficulty.
Let me quote the website about the different levels:
I nivå 1 dominerar ofta bilderna och det är lite eller mycket lite text.
I nivå 2 texterna längre. Men handlingen är enkel ...