Linda learned English with her walkman.

Linda learned English with her walkman.(意思是Linda是用随身听来学习英语的.)这里的"with ",意思是某种工具或手段.不可以用"by",虽然两者都有共同意思,但用法不一样,如果用"by",应该是by+动词—ing.意为：“通过…,靠…,凭…”.Linda learned English by using her walkman.
你参考下面资料区分下"with 和"by"的用法就知道了.
with表用某种工具或手段
I cut the apple with a sharp knife .
我用一把锋利的刀削平果.
Tom drew the picture with a pencil .
汤母用铅笔画画.
by+动词—ing.意为：“通过…,靠…,凭…”.
如：by waiting/practing/begging/working/imitating等.
He gained his wealth by printing works of famous writers.他通过印刷著名作家的作品而获得了巨大的财富.

可以，意思通过随身听来学英语

不可以。

不可以。
如果要用by，应该：
Linda learned English by using her walkman.