Did King Claudius know that Hamlet knew his secret?

I really don't think that Claudius is that smart to figure out that Hamlet knows. He is suspicious about his actions but he seems dense in my mind. For example, in Act 3.1 he urges Rosencrantz and Guildenstern to keep questioning the lord Hamlet to share his reasonings as to why he is turning mad all of the sudden.

"With all my heart, and it doth much content me
To hear him so inclined.
Good gentlemen, give him a further edge
And drive his purpose into these delights."

If he thought more closely on the subject that rakes at his mind every minute of the day, he should realize that Hamlet knows every plan that the King has in order for him to speak. Nevertheless, Claudius keeps at it, determined to find out what is the matter... not even noting Hamlet when he is overhearing his discussions about the lord in question.

Did Hamlet love Ophelia before?

I believe that Hamlet did, indeed, love Ophelia before he knew anything about his father's murder. For instance, in Act 1.3, Ophelia reveals to her over-controlling father that Hamlet had confessed his love for her. Isn't that obvious enough that he loved her deeply? But also there are the love letters. In Act 2.2, Polonius talks about the many love letters that his daughter had received from the lord Hamlet prior to his madness but only mentions the one where he purposefully wrote a terrible one for her. Though he was a complete jerk to her in Act 3.1, the repeated lines of "go thee to a nunnery" shows his wanting for her to be his and only his, right? This is ignoring the fact that he made two women into one person... which is just nasty.

Act III Scene i and ii

In the course of these scenes, the prince of Denmark seems to me less mad than everyone thinks. Seemingly faking it, he is receiving information from all around him. Though he speaks of suicide and regarding Ophelia as a deceiving woman, he seems to still love her deeply as shown in Act III Scene i lines 122-130.

Yet in Act II Scene ii, Hamlet is overly calm about what he is planning on doing the play in "honor" of the King. He reveals most of his plan to Horatio yet seemingly becomes his normal loner self before becoming "mad" once more as the others enter the scene. While the play goes on, he cunningly interprets the "play" while the others watch in wonder. Hamlet is thrilled as he successfully gets a reaction from Claudius. Hamlet then returns to his normal state of mind and confronts Horatio, wanting his interpretation of the who incident.

Yeah, I know only five sentences were asked but I felt like I needed to say more for some odd reason.