Is it a relatively big fee buying Bitcoin on bitcoin.com? I bought some Bitcoin on Robinhood for $0 fee, and about $2.99 fee on Coinbase.com, but since bitcoin.com seems like an official website, I tried installing the app to buy some Bitcoin, but for $180 of Bitcoin, the fees are like $13.50 + $2.32 = $15.82   (as paid by Apple Pay).
It seems such as big percentage (8.3%) of fees just to buy $180 of Bitcoin.  Is that just the way it is on bitcoin.com or any method to make the fees at most about 3%?
bitcoin.com seems like an official website

No, it is in no way official. If I remember correctly it was started by a group of people who created a new cryptocurrency by forking Bitcoin, they wanted to take over the name Bitcoin for their altcoin. They are not well regarded by the Bitcoin community. Their altcoin is not Bitcoin
There are no officials and no official websites for Bitcoin. This is because Bitcoin is intended to be completely decentralised.

Is it a relatively big fee buying Bitcoin on bitcoin.com?

Your numbers for other currency exchanges suggest that this is the case.

Is that just the way it is on bitcoin.com

Yes, apparently they are a business that charges higher fees than some other businesses.

how do I get a Bitcoin wallet?

A good place to start is https://bitcoin.org/en/choose-your-wallet but also see
I am new to Bitcoin, how can I get started?