How does Ethereum Smart Contract work on Mobile Client

How does Ethereum Smart Contract work on Mobile Client

I want to deploy a smart contract on server and interact with it using mobile client. I'm not familiar with how does that work but after some research, I found something like below: 

I want to deploy a smart contract on server and interact with it using mobile client. I'm not familiar with how does that work but after some research, I found something like below: 

If we compare communication through web services in mobile client, then pretty much everything is same expect in Smart contract, is no database or deployment service as the result of decentralized nature of the system. Is that right? We can connect mobile client to smart contract using some library like web3 which would essentially work with Json RPC or websockets.

But what if I don't want to connect each mobile client to smart contract using library like web3? Instead, what if I want to have a HTTP server and then it would connect to smart contract like below? 

Is that possible? If yes, then how can I do that?

My second question is regarding deployment. In the centralized server scenario, I would have database deployed on some service like AWS etc. I could estimate the deployment cost. I understood that we have to deploy smart contract on Ethereum mainnet which will cost some x amount of Ether. But then I found out that my users will have to pay for each computation. What if I want to bear all the costs? How can we estimate such costs?

Please guide me on the above questions.Thanks.

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