user133898: How can I run a Bitcoin SPV node? Am I able to run SPV nodes with Bitcoin core? If so, can I use JSON-RPC by sending requests to full nodes? I couldn't find a good way to retrieve transaction data other than installing a full node.

user208: 
How can I run a Bitcoin SPV node?

You run Bitcoin SPV software. They're often called "lightweight clients" or "lightweight wallets". Several mobile wallets implement SPV validation, as does Electrum (though note that Electrum is not technically a node; it connects to Electrum servers, not to P2P nodes).

Am I able to run SPV nodes with Bitcoin core?

No, Bitcoin Core only implements a fully-validation node.

If so, can I use JSON-RPC by sending requests to full nodes?

No, Bitcoin Core's JSON-RPC interface is designed for the owner/operator of the node to connect to their own trusted node. It's not designed to be exposed to third parties.
Furthermore, the JSON-RPC interface is specific to Bitcoin Core. Other software will have different ways of communicating or interacting with it.

I couldn't find a good way to retrieve transaction data other than installing a full node.

That's pretty much by design. Bitcoin is defined to minimize trust; if you want validated data there is really no way but validating it yourself using a full node.
The alternative is trusting other parties to do it for you. If that security model is acceptable to you, with the security and privacy risks that entails, you can e.g. use block explorer websites, or hosted wallets.

133898: <p>How can I run a Bitcoin SPV node? Am I able to run SPV nodes with Bitcoin core? If so, can I use JSON-RPC by sending requests to full nodes? I couldn't find a good way to retrieve transaction data other than installing a full node.</p>
 208: <blockquote>
<p>How can I run a Bitcoin SPV node?</p>
</blockquote>
<p>You run Bitcoin SPV software. They're often called &quot;lightweight clients&quot; or &quot;lightweight wallets&quot;. Several mobile wallets implement SPV validation, as does Electrum (though note that Electrum is not technically a node; it connects to Electrum servers, not to P2P nodes).</p>
<blockquote>
<p>Am I able to run SPV nodes with Bitcoin core?</p>
</blockquote>
<p>No, Bitcoin Core only implements a fully-validation node.</p>
<blockquote>
<p>If so, can I use JSON-RPC by sending requests to full nodes?</p>
</blockquote>
<p>No, Bitcoin Core's JSON-RPC interface is designed for the owner/operator of the node to connect to their own trusted node. It's not designed to be exposed to third parties.</p>
<p>Furthermore, the JSON-RPC interface is specific to Bitcoin Core. Other software will have different ways of communicating or interacting with it.</p>
<blockquote>
<p>I couldn't find a good way to retrieve transaction data other than installing a full node.</p>
</blockquote>
<p>That's pretty much by design. Bitcoin is defined to minimize trust; if you want validated data there is really no way but validating it yourself using a full node.</p>
<p>The alternative is trusting other parties to do it for you. If that security model is acceptable to you, with the security and privacy risks that entails, you can e.g. use block explorer websites, or hosted wallets.</p>
