I am keeping a pet hamster.
And this sentence:
I keep a pet hamster
Sounds exactly the same to me, any minute difference, if any at all? Thanks!
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1: I keep a pet hamster
...is slightly "unusual" phrasing (compared to I have a pet hamster), so if it came from a "careful" native speaker it would probably carry some "context-specific" nuance over and above the bare literal sense. Perhaps the speaker is implying ...for the benefit of my mental health1 or something.
2: I am keeping a pet hamster
...is very unusual phrasing. The main thing implied by Present Continuous here is this is a current activity (that doesn't necessarily extend far into the past or future). Perhaps the speaker is temporarily looking after a friend's hamster.
Note that although Simple Present I have a pet is the idiomatic standard here, the keep version is "okay-ish". And we can easily imagine contexts where Present Continuous I am keeping a pet hamster (temporarily, for my friend) is "acceptable", but there's really no credible context where a native speaker would say I am having a pet hamster. That's an "Indian English" shiboleth which should always be avoided.
1 This suggested "reason for using keep rather than have illustrates the more general point. We tend to keep "working/food animals" (security dogs, farm cats, chickens, pigs), whereas we have animals primarily treated as pets/companions.