Low reps for strength and high reps for muscle gain. For beginner I'd suggest 8-12 reps range. Reason being it is light enough that you can do it with correct form and heavy enough for your muscle to grow.

Once you are more experienced you can try lifting heavier like 5- 8 reps.

1-5 reps are usually for strength training, doesn't really build muscle but still good to lift heavy once in a while.

Breaking into sets is good because you get to rest and recover. When lifting heavier weights you need to rest enough so that you can do the next set properly.

However, your question is for push ups. If you can do 30 reps easily then there is no need for rest.

30 reps is definitely too light for optimal muscle growth.

For smaller muscle group like bicep 12-15 is good.

If there is no heavier dumbbells then you make do with what you have.

Muscle will definitely grow but just slower.

Also make sure you eat enough so that there is calorie surplus if you want to gain muscle.

Maybe you should try doing the same reps for both arms so that no muscle imbalance in the long term.