Is it permissible for a Muslim girl to speak with a foreign Christian girl via Skype to improve her English language skills, and is this considered an act of allying with disbelievers (muwalat al-kuffar)?

Mere conversation with a disbelieving woman is not considered an act of loyalty to disbelievers, as the Companions engaged in buying and selling with them and similar interactions. There is no harm in addressing disbelievers in their language when there is a need or for the purpose of inviting them to Islam; this is not the detested "rattana" (speaking in a foreign tongue unnecessarily). The important thing is that the conversation does not involve glorifying their disbelief.