In terms of friendship, the answer is yes as evident throughout the franchise, both with regards to the Doctor and the Master and other Time Lords.
In terms of romantic love, Time Lords have also been shown as capable of this. The Doctor, for example, has been shown as in love with several companions over the years, though it is traditional that the character never actually says the words "I love you." Examples include Rose Tyler (per "Doomsday"), one of his four wives named River Song (per "The Wedding of River Song", et al), Madame de Pompadour (per "The Girl in the Fireplace"), Clara Oswin Oswald (per "The Snowmen") and Clara Oswald (per "Heaven Sent" and "Hell Bent", and according to Moffat the Doctor indicates his love for Clara in "Dark Water" when he says betraying him makes no difference as to how much he cares for her).
Other Time Lords known to have been in love include Andred, who fell in love with Leela in "The Invasion of Time"; the Doctor's granddaughter, Susan, who fell for David Campbell in "The Dalek Invasion of Earth", and the aforementioned half-Time Lord River Song (who addresses this fact directly in "The Husbands of River Song"). The Harold Saxon version of the Master is shown to have married a human woman in "The Sound of Drums" but it's unclear whether he ever had actual feelings for her.