Filing a patent which my research advisor will found a company on it
Disclaimer: I'm not a layer so the answer is not an advice but a collection of thoughts based on my experience. And each particular situation can have many facets which one with limited knowledge may not foresee. Also intellectual property law varies from country to country, so additional details would help answering.
I start from last question:

No, your supervisor can not exclude you from the patent as you are a coinventor. If she or he files the patent without you, you can claim against it in front of the patent office. Make sure you have some proofs of your authorship. If you had exchanged emails with your supervisor on this topic, it can be also useful. Note that in patent right public disclosure of invention leads to loss of patentability. In simple words if you tell someone (non-inventors) about invention and they can prove it, the patent application can be rejected.

The first one is the more difficult question. Here it strongly depend on your relations with your employer and country laws on intellectual property. In some countries having a contract with your employer would mean that intellectual property (IP) generated within this contract belongs to the employer. Depending on country you may keep parts IP of it or get only a bonus from employer. In situation you describe, it is difficult to give you an answer without knowing details of your contract and IP laws of the country. In any case typically the patent can be licensed to whoever wants to use (the startup company in your case) it by IP owner (inventors or/and your employer).


Hope it helps to proceed with more detailed search.