I have an echo dot (Alexa) and I would like to control what the alexa is saying from my computer (by typing it). I can synthesize speach using amazon polly, but can I also make Alexa say it and enable the blue glow while she is saying it as if she would respond to a voice command?
Yes. You can add capabilities to Alexa. These additional capabilities are called Alexa Skills. Please go through the following documentation for building Alexa skills using Alexa Skills Kit(ASK).
https://developer.amazon.com/docs/ask-overviews/build-skills-with-the-alexa-skills-kit.html
EDIT:
Alexa is basically based on the user-initiated conversation, hence it getting invoke without the user initiating a conversation defeats the whole purpose of it. However, Alexa Communications Announcements might be the very thing you are looking for. As it allows you to send announcements to you Alexa device using the companion app. It says,
Use the Alexa app on a mobile device to send recorded audio or TTS announcements.
From the Communicate tab of the app, select the Announce button. Then use either the microphone button to record an audio announcement (which will play in the user's voice) or the keyboard to write a text announcement (which will play in Alexa's voice).
This should do the trick for you.