You've asked important questions. The fact that you lost a toe nail after your 10K (runner's toe) indicates that your shoes were too small, causing your shoe to rub on your toe. Here are some suggestions.
Go to a good sports store to get your shoes. Don't go to a mall-type store. As you try on various shoes, the clerk should watch you walk and jog. Some of the better stores video tape your feet so you can see what they are describing as they discuss shoes with you.
Buy your shoes in the afternoon or early evening after your feet have had a chance to swell from your days activities. Be sure you wear the same stockings when you try out shoes that you will wear while running. Don't wear cotton socks, because they absorb water, and the soggy sock is more likely to rub on your feet and cause blisters. Wear synthetic socks that will wick moisture away from your feet. One of the places that I run is low and collects water after storms. I just run through the water (about 2 inches deep), and my shoes and socks get wet. However, because neither the shoes or socks absorb water, my shoes and socks dry quickly, and I've never had a problem running though those deep puddles. Good sports stores should also have good socks. However, I buy my socks from Costco at a lower price.
As you try on shoes, press down on the toe box. You want about half an inch between the end of your longest toe and the inside of the toe box.
Some shoes will need breaking in and some won't. So after you take the shoes home, walk and jog around your house for a while. For your first run outside in your new shoes, do a relatively short run of a couple of miles.
After you've selected your shoes, wear them around the store for a while and walk and jog in the store to try them out. If the store won't let you do that, go to a different store.
In 36 years of running, including four marathons and many, many 15-mile long runs, I've never had a problem with my shoes or socks. I've never put vasoline on my feet, and I haven't heard of other runners doing that. With the correct shoes and socks, you shouldn't need vasoline.
Concerning getting a larger shoe, that depends on the shoe. Good sports stores should have knowledgable clerks who will correct fit the shoes.
Here is the link to my shoe page. There are three types of running shoes, and you must buy the correct type. Wrong shoes are a common cause of injury.