Sometimes buds, pedicels and even peduncles will abort but I never remove them on purpose. The only pruning I do is to the stems if I want to root them for additional plants or make a fuller basket by planting the cuttings in with the original plant.
Jelinda: Your first photo shows both closed buds as well as opened flowers on the same umbel. I've had this happen on a few hoyas, sometimes a few buds will open and then maybe two or sometimes three weeks later the rest will finally open. But I've had hoyas that have sometimes aborted buds, peduncles and pedicels as well. I don't know why it happens, possibly culture issues, sudden change in air temp's etc. but they eventually produce new ones and bloom again.
Here is a H. kerrii and H. carnosa bloom that took awhile for all of the buds to finally open up:
@Alohahoya Carol is our very knowledgeable Hoya guru and hopefully she will confirm or correct my description and labeling of the flower parts in my photo's below.
The Peduncles are sometimes shaped like a little microphone and some folks refer to them as bloom spurs because they kind of resemble little spurs, but the correct name is peduncle. The Pedicels are the thin stems that emerge from the Peduncle; the flower buds/inflorescence emerge from the ends of the pedicels.
The photo's below are H. carnosa and H. merrillii where I notated and drew arrows showing the Peduncles and Pedicels. In my H. carnosa photo the peduncle is quite small and not quite visible but the H. merrillii photo shows different sizes and shapes of peduncles.