Is Earth vs the spider in the public domain?

Answer 1

The character of the Spider cannot be copyrighted. Only expressions of an idea are eligible for copyright protection, not the idea itself. It does appear that the character of the Spider, however, is registered as a trademark of the Argosy corporation.

As to the original stories, provided that all the necessary applications & extensions were filed no the first of the Spider pulps would not fall into the public domain until the year 2038 (presumedly the stories/artwork were done as "work-for-hire" & as such would have a copyright term of 95 years post-publication).

Answer 2

No. The copyright was renewed.