Exactly, bitcoin is never overpriced, you can even decide to buy any amount worth of bitcoin, like buying just $100 worth of bitcoin.
1. Since I have started my crypto journey I have never used up to 1 dollar for a gas transaction on Bitcoin, maybe this is possible if I moved a million dollars worth of Bitcoin I don't know.
Bitcoin does not use gas fee as transaction fee, bitcoin is not altcoin. I have used up to $1 before for bitcoin transaction, I remembered the last time I paid high was when China ban bitcoin mining, the mempool got congested at the time. Two or maybe little more weeks after the time, and most often, I pay low fee for bitcoin transaction, less than $0.1 but this depends on how congested the mempool is, the transaction input and output in vbyte (the weight of the transaction) and also the price of bitcoin. As mempool is not congested (around 1 - 4 sat/vbyte), with 1 input and 2 outputs, and as bitcoin price is at around $38000, I pay around $0.06 - $0.25 as fee.
2. I believe that Bitcoin is still very cheap, God only knows how much the gas fee would be if other altcoins like ETH and Tron move up to 65,000$ per coin.
Yes, bitcoin transaction fee is cheap. I do not know much about altcoins, but I think the fee should also be cheap if the mempool is not congested.
3. There will come a time where satoshi's ( 0.0000*** BTC ) will be worth a lot, buying 1$ BTC every day or two can still be huge someday, you are not too late.
Maybe, but I think it is unlikely. You can use lightning network which is one of the reason for the onchain transaction not to be as high as it supposed to be. There could also be more solution just like from uncompressed legacy address transaction to compressed legacy, from legacy to nested segwit and from nested segwit to native segwit, and also the recent upgrade which is pay-to-taproot that reduce the fee for multisig transactions and also making input consolation possible with lower fee.
Don't let anyone fool you that Bitcoin price is too high, remember, it was high at 5000$, 19000$ some years ago, Bitcoin is the new Gold and you don't have to own or buy a gigantic Gold to be rich, just have some.
Not even people are fooling people, it is centralized exchanges like Binance and others that are fooling people to let them make use of their altcoins which they are calling bitcoin, but not actually bitcoin but altcoins, so the people that were fooled will pass wrong information to other people that bitcoin transaction fee is high. As people can pay for bitcoin transaction fee with less than $1 on reputed noncustododial wallet, exchanges can charge $25 or higher as bitcoin withdrawal fee.
About bitcoin being new gold you referred to, I perfectly agreed to that, although, I will not call it gold because it has a limited supply and that gives it more deflationary advantage. More adoption, more marketcap, more price increase. Also wiith more price increase as it is always compared with inflationary fiat.