Like you only for your meal ?

I have been dating a girl for almost two months. We usually met once every week. We typically went to dining together, but also been to museum and amusement park. She likes fine dining, and most often we went to restaurants which I considered as quite expensive.

At the beginning I thought it's still fine. But as time went by, if we were to discuss about where to eat, she would often prefer restaurants which is fine dine type or near to that. And I start to feel pressure on sustaining this style of going out.

I have tried to communicate and discussed with her about my concern. But she considered it as normal for dating and started to feel unhappy when I was discussing about it.

The problem is, I actually even not sure if we are in a relationship. At times, she was fine with me to hold her hands. But sometimes, she would only allow to hold hands for a short time. She is kind of reluctant to kiss and she only gave me a good bye kiss but with a face mask. She said she would want to take things slowly.

While we were eating, from time to time she would check her phone and messaging with others. But in between our dates, if I were to chat with her in messaging, her reply usually was quite slow and I felt like she was not so into messaging.

Although she is still willing to go out to dine with me, but somehow I start to feel like she actually just like the meal rather than me because so far I am the one to pay for all the dining and any other activities we do.

Am I really taking things too fast, and is this style of dating normal ?