Your Question #1: Does adultery of the heart as described by Jesus in Matthew 5:28 constitute the same form of "sexual immorality" given as an exception for divorce being permissible in Matthew 19:9?
No, but they're "kissin' cousins"! The thought is father to the deed. If you find yourself repeatedly fantasizing about "having an affair" with that woman at your job with whom you seem to have a mutual chemistry, don't be surprised if you find yourself in bed with her someday.
Is actually committing adultery with one's body worse than committing adultery in one's mind? Of course. Just as it is "less bad" to think about smacking someone than it is to haul off and actually smack him! Some sins are worse than others, and to say they're all the same is nonsense. Now yes, one sin, be it in thought or deed, be it big or small, will keep us out of heaven, unless Jesus interposes His precious blood. That's the legal aspect, if you will, of sin being followed by death, unless Jesus steps in and bestows His forgiveness on us.
Is committing adultery in one's heart, then, grounds for divorce? Possibly. It depends. If the adultery takes the form of an addiction to pornography, such that bills are not getting paid because bill-paying money is being wasted on smut, then possibly yes. However, if the husband is willing to get help with his addiction and does in fact get the help and make strides in eliminating it from his life, then in my opinion his wife might also have "grounds" to give him another chance, forgive him, and move on from there.
If, on the other hand, she is simply not willing to forgive him, or she simply can't find it in her heart to forgive him, then I would recommend they both get counselling, both together and separately. A wife who goes full steam ahead with a divorce without even giving her husband a chance to confess, repent of and forsake his sin, is likely either not a Christian, or a very carnal one, and may be looking for an excuse to get out of the marriage. She's evidently forgotten the part of her marriage vow that says,
"for better or for worse."
The same goes for a husband whose wife has cheated on him. Divorce need not be automatic, if there is a willingness to forgive and to be forgiven. If there's no willingness, then perhaps the effects of the sin have spilled over into the family (such that the husband has molested a son or daughter or has committed some other heinous sin), and divorce seems to be, in the opinion of a godly counselor or two, the only way out, OR, the sinned-against spouse is too carnal to forgive (or the sinning spouse is not willing to repent).
Your Question #2: In John 8:3-11 Jesus declines to condem a woman caught in the act of adultery and commands her to leave her life of sin. If she fully repents of her previous act(s) of adultery, would the exception for divorce given by Jesus in Matthew 19:9 still apply?
That depends on whether or not her husband wants to forgive her. If he doesn't, then according to Jesus he is allowed to divorce her. BUT, again, he is not required to do so. If the adulteress is genuinely repentant (and John 8 does not indicate one way or the other as to whether she was repentant, though it would appear that Jesus, being able to "read" people and know their thoughts and motivations, knew that she was repentant), there is still the possibility of forgiveness and restoration of the relationship.
Your Question #3: Assuming the answer to No. 2 above is No, at what point does the marriage covenant become re-established?
The marriage covenant is renewed, as you put it, when the spouses agree to a verbal contract which stipulates that the husband will forsake his cheating ways, and the wife will forgive his past infidelity, but only with the understanding that if the husband commits adultery one more time, there will be a divorce. Here, Jesus' words about forgiving seventy times seventy would not apply, in my opinion. Marriage is too sacred a thing to allow for seventy times seven infidelities.
Now, a second, third, or fourth adultery does not necessarily require or necessitate a divorce, but I think even Jesus would say after the second adultery, "Enough is enough. Your husband is neither able nor willing to repent of this sin, so seek a divorce if that is what you think God wants you to do, and you have a Holy-Spirit inspired peace about it."