Is it normal that my boyfriend still has feelings for his ex after 3 years?

If you seriously trust him, then let him meet with her. If you are truly uncomfortable with it, then let him know how you feel about it. His response should indicate his intentions with her.

I would let him know how you feel, without trying to influence his decision whether to see her or not. Forbidding him to see her will work against you, as we all love to do that which we are not allowed to do. It must be his decision not to see her.
Better you find out his character now, than after you are married.

He has no reason to go rekindle that flame. He's hoping to fuck her, now that she's back in town.

Don't let him go and see her. I can not accept that any decent man being true to a woman would 'want' to go see his ex. If he respected you and your love, then why risk exposing himself intentionally to a woman whom he already has had strong emotions for?

You shouldn't read his texts.

Be upfront and ask him if he still cares for her. Don't act jealous or you will push him into her arms.

You have to be honest with how you feel about him seeing his ex-girlfriend. You will know his intentions if you talk it out with him without sounding too possessive. If you trust and love him enough, then this might not be a problem. But again, you have to tell him straight of how you feel about it. For me though, exes should stay as exes and better left in the past. Just ask him why he wants to meet his ex-gf again.

Let him see her, if he tells her he wants her and she turns him down, he'll come back to you and if she says yes and he leaves you, well I guess you're fucked

Yes, it's normal that your boyfriend misses his ex, especially after chatting with her and talking to her. And in my opinion, letting him see her would be the worst idea you could ever think about! And he might end up cheating on you with her. From my experience, I realized that all guys are the same, we all miss our exes, and the moment we see them, every bit of feelings relive in our heart. So make sure, don't let him see her or meet her, for the sake of your relationship

Let him communicate with the other woman. If he truly loves you, he wouldn't leave you despite the other woman's presence; if he chooses the other woman, dump him/hurt him/shout at him(or even burn his house LOL). SRSLY, just leave him. it will be painful, but him leaving you only means he doesn't deserve you - you deserve someone who will love you the way he loves that other woman.

The truth is, nothing will stop them from seeing each other again if they have mutual feelings so I'd just let him see her. If he truly wants to be with you, he won't get with her. You really have nothing to worry about either way because if you don't let him, then he may be lying to you and himself by staying with you and if you do let him and he actually goes with her, at least you know he wasn't attached to you as much as you to him.