I think what's happening to BNB gas fee is just like the same scenario with ethereum gas fee that when it get more popularity from the crypto-space and many crypto enthusiasts are using the blockchain it gets crowder and gets more traffic that makes its gas fee high. I think now that BSC is now getting more attraction and getting plenty of projects' interest it will also begin to have traffic that makes its gas fee to be higher as well.
Of course. The more popular a blockchain network becomes, the more the network load will be. This translates into higher fees and slower transaction confirmation times. It's up to developers themselves to help scale the blockchain in question for fees to remain as low as possible. I think BNB shouldn't have a problem with fees in the long run, since it's scalable by design. Considering that Binance controls most of the network, it should be easy enough to introduce a network upgrade that would keep fees as low as possible.
While gas fees on BNB are increasing, they're certainly much lower than those on ETH. I guess BNB still has an advantage over ETH in this regard. There are many other smart contract platforms on the market right now, so high fees and slow confirmation times shouldn't be a concern for people. If both BNB and ETH get clogged up, there's always the choice of TRX, EOS, ADA, among others. What matters is decentralization. As long as projects focus on being decentralized, they will stand the test of time no matter what. Just my thoughts