Is one considered an infidel for abandoning prayer on some days after repenting, and is their first repentance valid, and must they perform ghusl again to enter Islam?

Sincere repentance is obligatory for abandoning prayer, as it is one of the gravest sins. Abandoning prayer is not considered disbelief according to the majority of scholars. Neither an apostate nor an original disbeliever is required to perform a ghusl (ritual bath) to enter Islam, unless they have incurred an impurity that necessitates ghusl.