Assalamu Alaikum Warahmatullahi Wabarakatuh,
Just to touch very briefly - One of the qualities of "Sincerity" is having yakeen whilst making Dua. This means you're not trying to test Allah by saying well let me see if it would work - no as a believer we need to put full trust in Allah azza wajal whilst saying the Dua(s), because in Surah Ghafir [40:60] Allah azza wajal says: And your Lord says, "Call upon Me; I will respond to you."
Secondly - to increase the "Sincerity" a highly recommended step - In the Quran Surah 7 Verse 180 Allah azza wajal says: "And to Allah belong the best names, so invoke Him by them. What do we learn from this? Please try to memorise some of Allah azza wajal Names and Attributes and call upon them. Call upon Him by His Names: The Generous, The Beneficent, The Munificent, The Accepter of repentance, The Forgiver, The Powerful, The Free of Want and The Omnipotent. Call upon Him by those names, sing His praises by them, raise your hands towards Him with those supplications, and approach Him wholeheartedly.
For example, whilst asking for forgiveness in your Dua(s) - you could begin by saying "Ya Ghaffar" (The one who constantly forgives) please forgive me all of my past sins, including Major Sins and Minor Sins, and that I know of and that I don't know of. Similarly, when asking for guidance - you may begin by saying "Ya Haadi" (The Provider of Guidance) please guide me and keep me steadfast in your religion.
Please remember us in your Duas.
Jazakallahu Khair,
DR