Speaking to Tenchou/ superiors at job?

Hi there! This is kind of a grammar/cultural question that I'd really love some advice with!

I recently started working at a Japanese restaurant in my city, and many of the staff are Japanese or speak Japanese. I believe one of the qualities that got me hired is my Japanese studies- I have been out of practice for a while now but I'm a beginner at about an N4 level. However, I think I've disappointed my Japanese boss because so far I've been far too nervous to break out any Japanese!

I'm mostly anxious about making sure my speech is respectful enough when speaking with the other employees. I'm the newest hire and also the youngest, so I want to make sure my keigo isn't deplorable. I've never been to Japan and I've been out of a formal Japanese class for a while so my immersion has been lacking and so I'm relying on self-study at the moment!

Can anyone help me with what titles to use when addressing my fellow employees? I have two 'managers' that own the store- a Japanese man and his wife (who doesn't speak Japanese). I believe the restaurant is actually really owned by the woman. c: Can I refer to them both as '店長'? Or perhaps the woman with her name + さん, as I think I heard another employee refer to her that way as she doesn't speak Japanese and -san is easily understood.

Also, there are the chefs. These men (about half speak Japanese as well) have been working there for many many years and are also much older than myself. What is an appropriate way to refer to them? Is there a title for chefs, or a superior higher than 先輩? I'm actually really intimidated by these guys since they're very surly and I'm not too sure if they're very fond of this new 白人 employee, so I want to make sure to be very respectful!

And for general purposes, what type of speech is polite enough? I'm still rather a beginner, and although I'm technically at a level past Genki I, I'm going through it from the start to refresh my skills after being out of class for a while. Is the polite form taught in most intro materials {～です、～てください、～ます) polite enough? I assume as a gaijin they will understand my skill level and give me some leeway, but I am very excited to have this job opportunity and want to make a good impression as I improve. My manager bid me a さようなら a few nights ago and I got about halfway through a さようなら reply before I stopped myself and choked out a しつれいします instead, as I remember we never replied to our teacher with sayounara but shitsurei shimasu instead as it was more polite.

Can anyone give me some specific advice? Thanks in advance!

If your colleagues call him 店長, it's the best choice. Similarly, it's OK to call his wife, the chefs or all your colleagues "name + san". As for polite words, yes, those polite forms and 失礼します are appropriate.
I think you don't need to be too much anxious about the correctness of the polite words. Your effort to show the respect towards other people must be conveyed.

Emmytofu san,

The best advice I can give you is to keep your eyes and ears open. I'm not saying that you should copy what everyone else is saying necessarily, but you'll get a good picture of how the shop is run. I've seen some businesses that are very informal and some that are so formal they border on a Monty Python skit. The more formal the business, the more strict the hierarchy will be (as a general rule).

In the meantime, use -masu/desu.
Other helpful phrases:
お先に、失礼します。(when you leave before anyone else does)
おつかれさまです。(when you leave...when someone else leaves...when someone gets back to the shop after running errands, etc.)
Others I'm sure you know like お願いします、ありがとうございます, すみません, おはようございます, etc.

You might be overthinking the situation a bit. Nervousness can be contagious (at best...misinterpreted as unfriendliness at worst), so go with the easy stuff where you can say it loud and with confidence (see above), ask questions (if the opportunity seems right), be helpful, and work hard. Sounds like fun.

The most certain way would be to ask the people where you work, don't you think?