Hey! Interesting question! In fact it's so interesting I'm not really sure what the answer is!
I'm not sure why 1a) and c) feel wrong, and I'm not even sure that they do. It's also the same with 1d) for me. I wouldn't be surprised if other people find it acceptable. I think it's something to do with the word 'plan'. If you change it to: "I offered you help", or "I offered you money" that sounds fine to me. It feels like you have to be able to 'take' the thing being offered somehow, in order to use 'offer'. For example, if you're talking about the physical document that your plan is written on, then I can imagine "I offered you my plan" would be fine.
With 1b) I think the problem is that you can only use infinitives with 'offer' if the subject of the main sentence is also the subject of the infinitive. For example, "I offered to tell you my plan" or "I offered to let you consider my plan" are fine, because the subject ('I') is doing the 'offering' and the 'telling/letting'.
I think 2a), b) and c) aren't right either, but for different reasons. For 2a) and c), I think the problem might just be that you can use an indirect object like that with suggest. Rather, I think it has to be like in 2d): "to you". For 2b), I think the problem is that you can't use infinitives with 'suggest'. Instead I would say: "I suggested (that) you consider my plan".
Hope that helps!