Speeding that also involves reckless endangerment is obviously sinful.
I think that minor speeding that is not reckless is not sinful. Several other threads here on the subject have cited priests in confession telling them as much (for example, forums.catholic.com/member.php?u=22071). Posters speaking here to the contrary are presumably saying they know more than the priests, or that someone is lying.
The Catechism never explicitly states we must obey the laws, rather it emphasizes deference to legitimate authority as a logical extension of the Fourth Commandment. This is normally accomplished by obedience, but I would argue not necessarily so, and I think this is what the priests were getting at.
I find no false dichotomy in saying that I can transgress a law but still defer to its authority to it as long as I submit willingly to whatever sanction is legitimately prescribed. If a cop wants to pull me over for going ten miles, or even one mile, over the speed limit, I will submit since they are fulfilling their lawful duty. I may or may not consider it bad “luck”, but I will very respectfully submit to cop and judge in that instance. I will not flaunt my legislature and break it for no reason.
Similarly, I will not drive on five miles out of my way to turn around if I only have 190 feet to lawfully get into a turn lane instead of 200. If inconvenient, I will happily keep a library book over the prescribed day and pay a fine rather than feel obliged to return it. I will jaywalk if safe and not scandalous. If I live under a truly silly law (google those), I will feel no compunction for transgressing them, but will pay my debt (or argue its unconstitutionality) if needed.
This makes sense to my conscience at any rate. I normally don’t speed myself, unless late to an appointment, in at least some proactive deference to the state, and even then around five mph max. Those that claim all unnecessary speeding is a sin need to confirm on the record here that the priests speaking to the contrary were wrong.
As to your second case, I’m on shaky ground, but I think that the same standard of deference to either the house rule or the consequence is warranted, and that you may be morally permitted to break the letter of the rule if it is unreasonable, at least as applied. It’s a contract or license and people break the fine print of those all the time as they are given on a take-it-or-leave-it basis. I might stray a foot off a trail to pick up an interesting leaf. I might keep a rosary in my pocket for a bar exam even though it is not on the list of acceptable items. I might refuse to throw away chewing gum (whether in mouth or pocket) when walking into a movie theater. I might burn a CD onto my computer for archival purposes even if the terms prohibit it. I might bring a gluten-free cracker into an amusement park if I’m not likely to find anything suitable to eat from the vendors. Let them sue me, and again I will defer to the civil authorities and to God if wrong.
In contrast, I would not take a drink to a restaurant (unless I buy another drink there perhaps) as that would not be fair to my hosts; their rule IS reasonable. I may consider bringing certain nominally prohibited items into a place that provides them, IF I consider their rates to be highway robbery. Even so, I will accept the consequences should it come to that.
If your conscience troubles you about a specific issue, definitely bring it up at your next confession. No harm in clearing it up. In the meantime, educate yourself (as you are doing here) and pray for further discernment.