Spearman's correlation on discrete data

I'd like to know if it makes sense to use Spearman's correlation on my dataset. Below are plots between my 3 variables :

Correlation plot (Spearman):

It seems it's pretty good but since I'm not from statistics I'm not sure. What do you think about it ?

• What do you mean specifically by Spearman has... problems with ties? (Kendall also has to manage "ties" in its own concept). What problems are these and how can they be managed. Could you expand on it or link to a discussion? Much thanks. – ttnphns Jul 7 '17 at 13:05