1.) Does it raise security problems to inject the plain text in the web page ?
Plain text is just text... there are no security impacts unless you start injecting code wich actually gets executed server side.Besides, what you are describing is client-side encryption/decryption. As a result, you'll end up with either plain text (=decrypted) or an block of "random" chars (=encrypted, guess base64-encoding after encryption and bas64-decoding before decryption will be safest when thinking email transfers)
2.) Does the web page (so Gmail) can detect such injection ?
3.)Is it vulnerable to a Man in the middle attack ?
If with "it", you mean your client-side encryption/decryption... no, as it happens CLIENT-side before sending any data anywhere.
If with "it" you mean "email traffic" when sending the data after encryption, you should know that — generally — email traffic "can" be vulnerable to MITM attacks. But as Google mail tends to enforce the use of SSL, I personally regard it to be safe from MITM attacks when users indeed keep SSL enabled at all times.
Talking about vulnerabilities, I would like to point you to two other things you should consider:
Depending on the crypto you are going to use, the way you are going to implement things can and will have an important impact on potential (crypto-related) vulnerabilities to consider.
Client machines of sender and/or receiver may be compromised — intercepting and transferring the decrypted data using malware like trojans.
Sending blocks of encrypted data via email can and most probably will put you on the radar of whatever governmental agency might be interested in the contents of such "encoded messages". It's been known for years, but recent news related to #prism reminded us all that "they" are actively parsing traffic like emails when something looks suspicious. I guess I don't have to explain that using cryptography isn't saying "I've got nothing to hide", but rather the opposite.
Last but not least, remember that - when it comes to software development in general - there are restrictions on the import of cryptography and there are even more restrictions related to the export of cryptography and export of cryptography in the United States) related to cryptographic implementations. Depending on your residence, these might have an impact on the product you are planning to create. Currently, many countries, notably those participating in the Wassenaar Arrangement, have similar restrictions. So, be sure to read the docs that come with the cryptographic algorithm(s) you are planning to use or you might face other kinds of trouble later on.