Q: Multiple issues with automatic car shifter

Since last winter, anytime it is cold out the shifter button sticks. Its typically when I first use my car in the morning on my way to work. When its quite cold out, the button sticks to the point that sometimes i cant pull it in enough to shift into reverse or drive. It's only when trying to shift out of park. So I'm wondering what that could be. But now, this just started last weekend, my car is delayed shifting into park (and into park only). On my dash is a little digital display that, when the car is one, shows the PRINDLE letters. Whichever gear you're in will have a black box around its letter. Well now, most the times I try to shift into park, I'll move my shifter into park, but it takes 5-30 seconds for that black box to appear around the P. While waiting the 5-30 seconds, none of the letters have the box so if i release the break, my car drifts. Please give me advice, I'm a single mom living paycheck to paycheck. I need to make this car last.

My car has 200000 miles.
My car has an automatic transmission.