Okay, that makes more sense. So with the Home Office's permission, we could marry in the UK while I am still a Tier 4?
Yep - when you give notice to marry, if you are on a Tier 4 visa, you may be referred to UKVI for further investigation (to make sure you aren't trying to marry just to get a visa), which can take up to 70 days instead of the usual 28 days.
If they approve you, you can marry on the Tier 4, and then switch to FLR(M) (in-country spousal visa) after the wedding.
Am I able to look for work/get hired while on a spousal visa?
Of course you can
. You can both work and study from the day you receive your visa, without needing sponsorship for either a Tier 2 or a Tier 4.
In fact, as you will have a visa that allows work, you should be given the same chance at a job as a UK citizen would be - i.e. you should be given preference for a position, along with UK citizens, before they can look to overseas applicants (so no need to meet the tricky requirements for work visa sponsorship).