Rav Gershon Edelstein, rosh yeshiva of Yeshivas Ponovezh, told the mashgiach of Ponovezh, Rav Rothschild, that tomorrow, even though it is Pesach Sheini, the Selichos of Behab should be said.
Rav Edelstein added that Avinu Malkeinu should he said as well, because the Chazon Ish held that Tachanun is said on Pesach Sheini.
Due to the current unstable situation in the world, Avinu Malkeinu should be said as well, said the rosh yeshiva.
{Matzav.com Israel}
אבינו מלכנו was composed exclusively for the עשרת ימי-תשובה and is never recited any other time of the year ever, as its content is simply not applicable to any other time of the year.
You are on target, that is minhag Ashkenaz.
Others however, say it on taanis tzibur during other times of the year too.
We have a minhag not to say tachnun during Hod, remainder of the week.