First off, 7kts on the nose and 4kt crosswind component is very restrictive!! My first solo limitation was 10kts, not a direct crosswind. Wind that is down the runway does not hurt, infact, I prefer to fly in 15kt winds down the runway vs 5kt winds (not gusty). All it means is you land slower!! In my opinion, you should ask your instructor about higher limitations. (Besides, we need more pilots that know how to negotiate )

Crosswind landing is great training, but personally I think any crosswind above a 5-7kt component should be done with an instructor during private triaining. My best story was the last flight before my checkride. We were landing on runway 23 with winds 230 @ 17 with another cessna. The other cessna went to runway 30 for crosswind landings. After his first landing, he calls "Hey, Cessna in the pattern on 23, want to join us on the crosswind runway?" I look at my instructor and say sure. A 16 knot crosswind component the day before my private. After about 3 landings, a Citation 5 called the uncontrolled field for traffic advisories. The other aircraft told him wind was favoring 23, but we were flying a pattern on 30. He accepted the challenge and made a decent landing. I think my 4th and final landing was better than the Citation 5!!

The experience was great for two major reasons. First off, I never felt 100% comfortable with crosswinds before that, but now I will do anything up to the max demonstrated crosswind component, even though I have fewer than 100hrs. Second, it was a great confidence builder right before my checkride. Crosswinds should not be avoided. Just they should be done with an instructor until you are really confident.