30-45 minute naps are fine at this age - although I would be beginning to try to lengthen naps by resettling. Also 90 ish minutes awake time between naps is fine too.
Sounds like you have a decent routine - feed - awake (90m) - sleep (30-45m) - awake (90m) - sleep (30-45m) - repeat. That all looks good so far.
So the key for you is consistent settling methods because at the moment they are all over the place. Pick one method - something that is sustainable long term with a view to progressing to independent sleeping - and stick to it.
If you are going for no dummy, chuck away the dummies and stop using them. If you are going to rock to sleep (I wouldn't recommend) then embrace it and have a plan long term for it. So consciously rock less vigorously or for shorter times so that the reliance gradually reduces over time.
Ideally I would settle baby to sleep in the cot for all sleeps at this age. So for a while you will be tied to the home until sleep is sorted. Use the same settling methods in the same place (cot) at every sleep time. Upon waking always try to get to baby as quick as possible and try to re-settle using the same methods (sleeping on your bed while baby sleeping in cot next to you makes this easy). 5 to 6 months old often marks the beginning of naps being extendable if have a re-settling method.
Pick-up-put-down often is very stimulating. How about settling in the cot instead? Could you sit/lie next to the cot and reach your arm in. Maybe a firm hand on chest. Or patting, stroking, tickling, shushing - whatever it takes. Just stay there as a constant presence reassuring and comforting until asleep. Same ever sleep, same every wake up.
The long term view would be that over time you gradually reduce the amount of reassurance needed. This isn't a quick fix though, baby may need your presence to go to sleep for many months yet, especially if there is no self-soothing with a dummy happening.
You need some form of sleep trigger - a comforter toy or blankie type of thing? Once older this is a snuggle thing that baby can find and cuddle to in the middle of the night to get back to sleep without you. Establishing a comforter takes attention, snuggle it into baby constantly when sleeping to create the association.