Are the characters of human influenced by his/her past life? or is it only because of present life? Is it mentioned in any Puranas/Vedas?
Definitely Hindu Dharma believes that the qualities of mind are inherited from past birth (not always the knowledge, which happens in rare cases). Just as past life environment and Jiva's participation effects this life same way present life experiences and participation is accumulating to qualities of mind.
There are lots of instances in Vedic lore:
पुरुषे त्वेवाविस्तरामात्मा स हि प्रज्ञानेन संपन्नतमो विज्ञातं वदति विज्ञातं पश्यति वेद श्वस्तनं वेद लोकालौको मर्त्येनामृतमीप्सतीत्येवं (मीप्सत्येवं) संपन्नः । अथेतरेषां पशूनामशनापिपासे एवाभिविज्ञानं....यथा प्रज्ञानं हि सम्भवः ।” (ऐ. आ. २-३-२)
Since Atman appears more clearly in human body, than any other beings. Human relates himself to trikaala, intellect guided karmas. His achievements can range from this world, other worlds (janmantara) and an attempt, even with his mortal faculties he aim to become immortal..... ones birth is according to ones collective intellect.
“वर्णा आश्रमाश्च स्वकर्मनिष्ठाः प्रेत्य कर्मफलमनुभूय ततः शेषेण विशिष्टदेशजातिकुलरूपायुःश्रुतवृत्तवित्तसुख मेधसो जन्म प्रतिपद्यन्ते” (गौ. ध. २-२-२९)
If people following their varna dharmas and Ashrama dharmas after giving up their body would enjoy in swargaloka, and then after that they would be born in unique place, jaati, kula, with good appearence, long life, knowledge, good conduct, money, happiness, good intellect.
The famous shlokas from Bhagavadgita.
Translation from Gita Press.
पार्थ नैवेह नामुत्र विनाशस्तस्य विद्यते । न हि कल्याणकृत् कश्चिद्दुर्गतिं तात गच्छति ॥6-40॥
Sri Bhagavan said : Arjuna, there is no fall for him either here or hereafter. For, O My beloved, none who strives for self-redemption (i.e., God- realization) ever meets with evil destiny. (40)
प्राप्य पुण्यकृतां लोकानुषित्वा शाश्वतीः समाः । शुचीनां श्रीमतां गेहे योगभ्रष्टोऽभिजायते ॥6-41॥
Such a person who has strayed from Yoga, obtains the higher worlds, (heaven etc.) to which men of meritorious deeds alone are entitled, and having resided there for innumerable years, takes birth of pious and prosperous parents. (41)
अथवा योगिनामेव कुले भवति धीमताम् । एतद्धि दुर्लभतरं लोके जन्म यदीदृशम् ॥6-42॥
Or, if he is possessed of dispassion, then not attaining to those regions he is born in the family of enlightened Yogis; but such a birth in this world is very difficult to obtain. (42)
तत्र तं बुद्धिसंयोगं लभते पौर्वदेहिकम् । यतते च ततो भूयः संसिद्धौ कुरुनन्दन ॥6-43॥
Arjuna, he automatically regains in that birth the latencies of even-mindedness of his previous birth; and through that he strives harder than ever for perfection in the form of God-realization. (43)
A suppositional reasoning for the above would be any prodigy whose achievements can be linked to his past life.