Is it considered a sin to constantly wish for the engagement to continue after performing the Istikhara prayer? And is my dream of my mother an indication that the first suitor is not destined for me?

Your eagerness for the suitor is acceptable as long as he is pleasing in his religion and character, and your supplication and efforts are permissible. Remember that goodness lies in what Allah chooses, so supplicate that He chooses for you what is good for your religion and your worldly life. You did well by praying Istikhara, for if a share is destined for you, it will come to pass, and if it is diverted from you, know that there is no good for you in it. As for dreams, no decision should be built upon them; what truly matters is what brings peace to your heart and becomes easy after Istikhara. "If any of you sees a dream that he likes, let him praise Allah for it and speak of it, and if he sees something else that he dislikes, let him seek refuge from its evil and not mention it to anyone, for it will not harm him."