Should I apologize?

You should apologize for not making a detailed plan and then ask her to hang out with you again

Since you asked her you should of been the one to make the plans even if you just gave her ideas of what you guys could do together then let her pick. That would of been nice. Since you don't know how it affected her I would still be polite and call her and apologize. I mean what if she purposly didn't make plans that day so she could hang out with you then you left her hanging sorry but that is kind of rude but easily fixable. And about her messageing you she probably didn't wanna look like she was desperate or annoying.

if all these questions were lingering in your head monday .regardless of her not calling .you should have called her anyways just to clear things up and see what was going to happen if anything once you realized the two of you didn't make plans when you agreed on monday before. I believe you need to apologize for not calling or showing up. And let her know that she can call you as well and let her know you were waiting for her to call. I guess.

You don't need to apologize but she might like it if you act like a gentleman by apologizing. Just call her back again and make a good plan

You asked her if she wanted to spend time together. Therefore you should have been the one initiating the plans and contacting her. Because you didn't it makes you look kind of rude. I would apologize.

good move that you apologized, because now she knows that you respect her.