Yes, it can be. Both "over the years" and "through the years" would mean that since the first (unspecified) year, up until now, the speaker has received a lot of love. In fact, "over" is used more often for time periods than "through" is. For example, you can say "over the past three weeks," but it sounds a little strange to say "through the past three weeks." In your example, there is no strong difference, but I think that "over the years" feels a tiny bit like the speaker will no longer be receiving love, while "through the years" feels a tiny bit like the speaker will continue receiving love. There is nothing specific about the words that says those feelings are correct, though, and other people might not agree with me.

Yes, you can replace "through" with "over". There is almost no difference. "Through" implies that you received love somewhat consistently during "the years". "Over" just refers to any and all love you received during "the years". You could also replace it with "throughout", which has the same meaning as "over" in this context. Also, "the years" implies you have been receiving love for a great many years. If you are referring to only a few years (less than 9 or so), I would recommend replacing "the years" with: 1 year : "this past year" 2 years: "these past couple years" 3-5 years: "these past few years" 6-8 years: "these past several years" any number of years: "these past X (insert specific number) years".