Two problems might be related. But now can not prove the relationship, you should consider separately.
There are two scheduled processing method. First is "Real" cron job. This is kicked from Operationg system. Second is "Virtual" cron job. This is that plugin do the specific processing at a certain interval by using web access.
"Real" cron will be run in a INDEPENDENT PROCESS. So, generaly, web access does not delay so much. However, "virtual" cron will be run in the middle of the site access by users. So, the process of "virtual" cron must end immediately.
If heavy virtual cron job is running in the specific plugin, your site will be locked at fixed intervals. You may be able to identify "cron plugin" by uninstalling third-party plugin one by one.