Short answer: Yes, yes and yes. BUT: A tire doesn't have an expiry date.
The reason for all three points is that the rubber gets harder over time and looses its grip / traction, especially on wet ground.
Keep in mind grip is not only important for acceleration and braking, but it also keeps the car on the street in curves.
Rubber not only gets harder, but also more brittle, and get this little cracks, which indicate an old tire:
However, these cracks are usually only at the surface and don't build an additional risk.
In the other question, it is stated that
Tires have expiry dates
but this usually doesn't mean there's a fixed date after which they are not allowed to be used any more. It merely means that life time of a tire is limited and there will be a time when you better change them.
Sometimes, there are laws limiting the maximum age of tires. In Germany, there is a single case: A trailer usually has a general speed limit of 80km/h, but some have 100km/h. Those need tires younger than 6 years.
But in general, Manufacturers say tires should be replaced latest after 10 years, while other recommendations start at 6 years.
What's quite interesting is that a tire doesn't start to age at its production day. Aging happens when a tire is inflated, exposed chemicals (petrol puddle at the gas station, ozone, oxygen, ...), sunlight and heat and when the tire is mechanically stressed. Or in short: When it's used.
A new tire stored uninflated, cool, dry and dark can remain as good as new for up to five years.
(But which tires are stored for 5 years before first use?)
I didn't find an english reference for this claim, but my last link at least supports this.