Is using the IP address faster than using the domain name?

Technically, yes. At least the first time. The first time your computer asks the internet "Where is this domain name located?" and some machine out there responds with its IP address.
However, when it gets this response back it keeps a copy (called caching) so it doesn't have to ask again for a while (these things CAN change, but rarely do)

So, if your computer currently has the IP cached, then they are equal. If you don't currently have it IP is faster, but only for the first time in a few days and only a few seconds

As for the question of how the fastest route is picked. There are several routing protocols, most of which take into account several different factors including load on a connection, bandwidth, latency, jitter, and distance. Several others are also possible. Long story short is that the routers of the internet are constantly telling each other that such and such link is down or I just got a new address connected and they have algorithms that the routers run to figure out which way is best.

N.B. A side note is that IP wont always give you access to a certain website: take for instance a site hosted on a hosting service. They rarely have their own specific IP address, but instead requests for lots of different sites could come into one IP. In this case the domain name being requested is used to determine which site to return to the requester

Both of the examples that you gave are correct. Inputting an IP address directly will bypass the need for a DNS lookup, but the advantage you gain by doing this could be pointless if you use an IP address to a popular website which brings you halfway around the world instead of to a server nearby. Ultimately, you wouldn't benefit enough to make it worth your while, especially since your computer will cache the response you receive from the DNS lookup, making the difference 0.