There are a number of points in the OP.
Firstly, Bitcoin can't compete with credit cards because there is no credit facility with . It doesn't lend itself to competing with debit cards either. Will it have to compete with payment processors? I don't believe it will - payment processors can eist as service providers in the Bitcoin world. So what about mobile payments? Do you really want to trust a globalist organisation like Apple with your money, or a Rothschild owned bank for tht matter? The whole point of Bitcoin is to escape from their clutches.
I believe that the only safe wallet is a node based wallet, anything else is just another banking operation, with all the caveats associated with bank deposits. At the moment it isn't possible to run a node on a mobile, but no doubt it will be possible in the not too distant future. One thing you could try is to tether a mobile to a netbook to run a node. You could synchronise the netbook over WiFi to keep your data transfer costs to a minimum.
I agree, as an experience with different wallet, I am currently using an online wallet too. It is easier to use it to convert btc to fiat here in our country. But really it is actually having high fees. Like for every Fifty dollars cashed out in our fiat has fees of 2-3 dollars. And dollars have high equivalent in our country.
It's the same as banks just more handy in y opinion.
Well, if security is the questions, they are safe. Especially with private keys. The walet I use sometimes have bugs but still good wallet.
Unless you have given someone or any website about your wallet and keys.