If you are not happy with your job how do you decide to quit?

Do you think it's okay to go to interviews while you're working and when you get accepted let your employer know that you will quit once you're done with your current project.

We have a dashboard that does stuff and one of the things that you can do is to turn these devices on or off. I the front-end guy made it look better and added some new visuals from the back-end data for better use. So I wanted to disable the off button if the device is off and vice versa. So I found out that when I turn it off or on let's say on, the device turns on but the data I get from the back-end still shows it to me as off because the data comes from the server and even though a device is on it updates the server about that periodically so I wait 10 seconds for that update.
The back-end guy tells me he just can't do anything about it and that's why it was like that at first. Then a few hours later this guy complains about this little space in between elements. Like dude, if you are such a perfect guy go find a way to make your thing work so the dashboard can have up to date information.

I really don't like showing off developers. Like the guy just changes color or invokes a function. Then instagram #superdeveloper #coding #ai. Dude wtf.

So I'm in my last year of university. The GPA is high. Did one internship the summer after second year in one of the best companies in my country. Third year in my department we do a semester long internship for 5 months, I joined a company and worked on back-end using Go. This was the spring semester and I wanted to continue working in the summer. The internsip company didn't tell me anything so I looked for a job. Found one that paid great, I was getting the salary a new graduate was getting. I worked as a full-stack there. Mostly prototyping, the company was new and I was in the R&D side. After 2 months the company had some budgetary problems and we parted ways. I was in the market again for part-time job in my senior year and because of my prior experience with Go, a friend mentioned me to a company executive he met and I had an interview and got in as a full-stack part-time dev. This was for some background information.

My story is;

The work is actually great in terms of what I do. I'm learning a lot here. The problem is that I'm having imposter syndrome for the first time ever. The projects are demanding and because that I'm part-time they take time to finish. There are no due dates or anything but sometimes the CEO is coming to me and saying "Aren't you finished with it?" or "Are you going to finish it soon?". Because that I'm more qualified in Javascript and React when they gave me my current frontend project I told them that its better if they give javascript/frontend projects from now on so that I can do a better job finishing them. What the CEO told me after that was, "Then hopefully you'll finish them sooner.". The people are nice and stuff like this only happened 2-3 times and the lead that I'm working with acknowledges my pros and cons and we have a good relationship, when I do something wrong he tells me why and how I can improve my code. But I just can't get over the syndrome and for some time I actually thought they would fire me when they get a full time dev.

Everything is great for some time. It's my fourth month and I think I felt this way because this is the most demanding job I have with senior year and also I didn't know people that well because I was the new guy. Although I still have concerns, have you ever felt this way? If you share tips or any recommendations I would feel great.

Thank you for reading.