Spike

This is entirely up to the team. Will estimating a spike help the team effectively plan a Sprint? If so, will estimating a spike in story points be beneficial? If the answer to both is "yes", then it could be worth experimenting. If the team tries it and finds that it isn't helpful, they can revisit for upcoming Sprints.

Personally, I've found timeboxing to be more beneficial than estimating spikes. However, some teams that I've worked with have had success estimating them.

Should we estimate a spike with story point (s)?

Does it represent empirically valuable work that can be Done in a Sprint and which therefore ought to contribute to the team's velocity?

Should we estimate a spike with story point (s)?

What if I said you should estimate it with colors. What if I said that you should not estimate the spike but should limit the effort to a specific timebox.  Would either of those be useful to your team? You should be asking your team the question because in the end, it is only their opinion that counts. 

My opinion is that if the spike exists on your Product Backlog, it should hold to the same guidelines of every other Product Backlog Item. According to the Scrum Guide that is 

... such as a description, order, and size.

Notice that the word estimate is not listed?  However, if you could use story points to represent size if your team feels it is the right thing to do. 

I usually advocate that a spike be given a timebox.  At the end of the timebox, discussions occur to decide if there is further work needed. If at any point before the timebox expires, the team decides that the spike has produced what is needed then stop. But the downside to this is that if you use story points to measure your velocity, you are doing work that is not going to be represented. That is where @Ian's question comes into play.  I am not a proponent of using story points to determine velocity but I will not get into that right now. 

Thanks guys!

We normally timebox a Spike within our Sprint but don't allocate any Story Points.