In my Skype/MSN conversations with Chinese mainlanders, language partner = 语言好友 【Yǔyán hǎo you 】。Literally it means language good friend but in context it means language partner.

study partner like as work partner.In Chinese ,we usually say an old couple as "老伴儿”lao ban er"to each other.

yeah,your direction is right.but we dont use this phrase usually instead of 同学.knowing the meaning is ok,there is no need to remmber.

现在主要是指一个人在学习期间的同学、同伴。

在求學期間的伙伴，通常指同屆同學。 後亦稱同一家族的同年級同學為「學伴」。亦作「學友」。 客家話則叫做「讀書伴」。