No. The halving can most certainly not have a direct impact on transaction speed. You don't seem to understand the difference between transaction speed (usually near-instant) and confirmation speed (10 minutes on average). The reason for which some people are experiencing unusual confirmation times is because they don't include adequate amount of fees.
This will then lead to the mining network difficulty decreasing, allowing for it to become more profitable to mine again (meaning that the blockchain can become more stable again)?
In the case that mining is not profitable for some miners, it would not be surprising to see (some) turn of their machines. In that case the difficulty would decrease (assuming that other 'groups' haven't turned on more gear). That does not mean "the blockchain can become more stable again". The blockchain always was and will be 'stable'.