Is what the questioner did, by communicating with a woman with the intention of marriage, and the resulting attachment of his heart to her and his feeling of something akin to ardent love, permissible in Islamic law?

The communication and exchange of affectionate words that occurred between the questioner and the girl is a sin that requires repentance. It is good for him to complete the proposal to her guardian and formalize the marriage contract with her. It is also sunnah to look at her before that. What the questioner feels towards her may be admiration or love, and he is not sinful for it as long as it adheres to the bounds of Islamic law.