I’m personally enamoured by the Spanish language but notice strong resemblances with Arabic in terms of vocabulary and even personal names. I understand this is due to the centuries of contact between the Arabs and Iberians. To what extent did Arab rule permeate into the Iberian languages like Español, was it superficial, restricted to vocabulary or did it penetrate into the grammar of Spanish language. Also, as Iberia was once heavily Muslim, I believe there was also a strong Persian presence in the peninsula. Have Iranic languages left a strong mark on Español? (Eg. “Vale” in Spanish and Farsi mean “Ok”).
I'm not particularly familiar with Arabic influence on Spain but I am an Iranist and speak Persian, so perhaps I can help you there.
I don't know how much you already know, but Arabic and Persian are unrelated languages, in the sense that the former is Semitic and the latter is Indo-European. Arabic influence over Persian largely consists of shared vocabulary (such as مشکل, meaning problem) although even here there are a some false friends, with some words acquiring different meanings in the proceeding centuries. Arabic was carried to 'Persia' through the Arab/Islamic conquests, and the adoption of Islam obviously was tied to the arrival of Arabic as the language of the Quran and therefore the word of god. However, Persian survived due to its literary status; as the vanguard of myths, legends, and oral histories.
That being said, I'm not sure that there was any kind of proportionate influence of Persian on Arabic. Culturally, the biggest Iranian footprint in Southern Europe is the Paradise Garden, which was a Persian concept taken up by subsequent Islamic dynasties and co-opted into their religion. Some of the finest examples can be seen in modern day Grenada and Seville.
Apart from Arabic, however, the largest single influence on the Persian language has been French. There are hundreds of every day loanwords in Persian that are directly lifted from French, primarily resulting from increased French presence during the age of European expansion in the nineteenth century, and the policy of Qajar royalty/elites sending their sons to Europe for their education. For example, the Persian for thank you is 'Mersi', the Persian for gift is 'Qado' and the Persian for Pineapple is 'Ananas'. It is more likely that Spanish-Persian similarities are a result of their common French influence.
Someone else may be able to come along and offer you more detail, but if you're interested in the impact of Arabic on the Persian speaking lands, I can recommend the first 2 chapters of Albert Hourani's 'A History of the Arab peoples'.