I can’t see your videos.
Hopefully the leg problem and the sneezing are unrelated. A bun can of course get a sprain etc from running around and binkying. Keep a close eye. Is her appetite good? Have you examined the foot for visible injury (a broken nail, a broken toe etc are things you can see.) If you touch the foot, does she react with pain?
The sneezing and boogers does suggest she may have a “bunny cold”. They are as a rule caused by bacteria of some type. Standard treatment is antibiotics, for example Bactrim, for 1-2 weeks.
Your other rabbit has been exposed if the two share a living area, but it is not uncommon for just one rabbit to develop symptoms. The bacteria that cause rabbit colds are very common bacteria that the majority of rabbits can carry in their noses but not become sick from. In very young rabbits, the immune defense is still immature, so they are more susceptible. Pet store rabbits can also have been brought up in less than ideal living conditions before they came to the pet shop, and being in a pet shop is also stressful. Stress takes a toll on the immune defense – luckily your bun now has a lovely home now where her rabbit needs are being met! (It is also believed that some rabbits are genetically predisposed not to be able to keep common bacteria in check – but this does not have to be the case with a very young rabbit.)
A vet would have to prescribe antibiotics.