How do I repair stoop/steps caulking? - pics inside

Hello, First of all, great site and I am learning a lot! My questions relate to how I might repair some patching between granite steps and the side wall of the stoop. The building is from ~ 1900 and most recent renovation was in 2007 at which point the patching between steps was replaced. You can see from the pics that this is crumbling away and needs work….probably due to freeze/thaws and snow shoveling in winter. There is a bigger gap toward the bottom steps and the side wall towards the bottom of the stoop due to some settling that has happened over the 100+ years … this is where the most problems are as you would expect …but it is in a number of places. So, my questions are: – What would you recommend that I use to patch this? – any specific product names/links? The current material is concrete-like in that it doesn’t seem to have any flexibility. I wonder if there was something that had more ‘give’ if it would have lasted longer. – Can I remove the bad pieces and just patch those? Most of the steps look to be OK but I suppose if it didn’t match closely the patch work would look bad. – Is this something a DIYer can try? I am not afraid to get my hands dirty and have done lots of plumbing, framing, dry wall, painting etc. but have never done concrete/masonry work. – How important is this strip/patch between the steps and stoop? Meaning, is it more cosmetic than functional? I can’t imagine that it was really preventing much water flow even when new but could be completely wrong in this. – Is this just a part of maintenance and should I plan that it will need to be patched/replaced every 6-7 years or so. Pics attached with a pen and quarter added for scale. The one next to the pen is by far the worst….the one with the quarter is more typical. Thanks for taking the time to read and for any suggestions that you might have. http://johnjohn2.imgur.com/all/