Opinion on whether it is a date or not

Hello everyone.

I am asking a question here because I need an opinion and I am asking it in this group because I would prefer an opinion from local people.

So I work with a company of only 7 developers. I have been getting close with a female coworker (we are both 31 years old).

I need an opinion on whether I am actually going on a date with her or just a friendly hangout. Here is the context:

Outing 1 (Only for Context) - She asked me if I am going to the food festival and I told her that we can go. We ended up going on the 9th of August, she showed some of her culture etc. It was a Sunday so she usually goes to sleep at around 8:30pm. We ate some food, played some carnival games and then left at around 7:30pm but she wanted to go to Valletta to hangout there. We ended up leaving Valletta at around 9pm. Then when we were approaching my car, she asked me if we can get milkshakes, which I accepted. We got the milkshakes and play fought on who is paying (she almost made me drop my phone). We got the milkshakes and got back in the car. Since it was getting late and I didn't want to keep her up, I was going to drive but she told me to not rush and drink it in peace which added 20-30 minutes. I ended up dropping her off at 10:53pm. She messaged me that she had an amazing time, etc

Outing 2 - We had a work event and this is where she broke the touch barrier, three times. Keep in mind that every time I am driving her, I am opening her door for her, but since I was driving another co-worker, I told her that she would have to open her door. That's when she put her hand on my shoulder and said that I am forgiven for this time. Then after the work event, me, her and three other coworkers went to a second location where we had some drinks. The three coworkers went by taxi while she came with me and my car. When we were crossing the road, a car was coming, she grabbed my watch area of my arm and told me to hurry. That was the second one. Then, the last one was when I dropped her off to her house at 1:30am, here, she hugged me for the first time and momentarily, I felt paralyzed haha

Next Outing - This Sunday. Her birthday was on the 17th August but she was abroad so on the 13th of August, when I was driving her home, I asked her out in a way that I told her that I would like to take her out for her birthday, regardless of it being late which she agreed and we are going to a fancy restaurant this Sunday. What she does not know though is that I am going to get her a flower and a cake.

Now here is the opinion, actually two opinions that I would like answered:

1. Is it a date?

2. Does she, or will she see it as a date?

Anything would help because I really like this girl. Some context about her is that she is an extrovert/introvert, loves her quiet time, goes on a lot of solo trips and hates huge crowds. Also she never had a boyfriend before either.

If you want more info, please let me know. Anything would help me in this situation because I am both confused and lost at the same time.

Thanks in advance