I've gotten a lot of my pets up to near level thirty, and they have yet to gain any more proficiency points, even though the guide says they should get them every five levels. can anyone explain what is going on to me?

on the pets profile page, if you scroll down there will be a button that says proficiency on it, click that, you have to set their element before you can set their proficiencies

Ok, so this seems to work, except it says that the next proficiency point is at level 60? and my pet is level thirty.
Also do unused proficiency points disappear if you level up without using them?

you get prof points at levels: 0, 30, 60, 65, 70 (and will get another at level 75, but nobody can get that because lv70 is currently the cap)

They remain right where they are- all pets- bred, caught, generated, whatever- between levels 0 and 29 have one point available for distribution, all pets lv30 to 59 have two, all pets 60 to 64 have 3 etc.

Currently Cora has one point of her two assigned (the "Available proficiency points: __" tells you how many points you have that are unassigned- once you assign all the points a pet has it says "Available proficiency points: 0")

Then why does the guide say they get them every five levels?

the guide is outdated- we linked some relevant posts where we explained it when we replied to your post in Tips for Newbies.