Ethereum hasn't yet released features which would provide something like SPV. Instead of SPV it will be called Light Client and the protocol for this being developed is called "LES".
More information on the ethereum github wiki.
Besides Browser Solidity (as @Rob Hitchens recommended), you could also develop smart contracts using Brownie. You could implement your smart contracts and test it on its local blockchain, where each transaction will be deploy right away and increment the block number.
Brownie: A python framework for Ethereum smart contract deployment, testing and
My impression is that SPV nodes cannot be validator nodes for the reason you stated (proof that ETH is securing the chain requires knowledge of blockchain state). With Bitcoin and node can convert to or from a SPV node to a full node (or vise vera) at any time.
SPV nodes can exist with Casper but they cannot be validating PoS nodes. SPV peers essentially ...
You can connect to a remote ethereum node such as INFURA, using the JSON RPC API, so you won't need to worry about maintaining and synchronizing a local node.
You can see this guide about using Truffle with INFURA
Disclaimer: INFURA Founder here.
Light clients are in the works, mostly working, though pre-alpha state. They are developed as part of the go-ethereum project. You can find more infos in the light client gitter channel: https://gitter.im/ethereum/light-client .
Further go-ethereum is starting to do experimental android and ios libraries covering a wide variety of features, among others ...
You can work with Browser Solidity. It let's you experiment with Smart Contracts, compile them, run them and debug them using an in-memory execution environment (default), or the real thing. https://ethereum.github.io/browser-solidity/
testRPC is a sort of blockchain emulator that's very popular with developers. It will initialize a bunch of accounts and ...
8. Simplified Payment Verification
It is possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he's convinced he has the longest chain, and obtain the Merkle branch ...
There are no light clients available yet. Some of are progress related to cpp-ethereum project.
For light weight wallet app do a hosted server side wallet. The server communicates with Ethereum node (geth). Each registered user has their own wallet contract. Mobile application communicates with the server over proprietary protocol.