How did you get the idea, that this is only YandexBot which produces these errors?
I suppose, any normal bot including YandexBot too, just opens some URL and reads the document available under this URL. Then it indexes any hyperlinks available under this URL, and spiders them, too.
I'm not sure that any server-side issue may be related to that. Definitely, no bot will even know that you have .htaccess
some snippets from the error text you provided, and for example, one of the first documents claims
it's Apache access rights related error.
it would imply that apache does not have read access on your /home/username directory.
The cause for this can be permission related, config related or ownership related.
Apache runs as user "apache", thus the directory must be +x for that user or group.
May be you may start from that... I'm almost sure it's not related to Yandex or any other specific bot.