If a person has these characteristics, are they considered a true believer in Islam?
1. Praising Allah in abundance by doing any acts of worships for a lengthy time whenever Allah gives and/or answers their calls.
2. Becoming very content when Allah provides them a person to be their guide and/or guiding a person to them. They consider those individuals as a treasure, under their protection, will defend and support them, and stay in touch for a long time.
3. Seeing those individuals who are important to them making mistakes and/or errors, they will become very disheartened of their actions, but they will try to help them to become a better Muslim.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

There is no doubt that whoever has these characteristics is blessed with great goodness. It is hoped of such a person to have high resolve that raises him to the sublime attributes of the true believers.

Allah, the Exalted, underlined in the Quran the attributes of those who deserve to be called true believers, as He says (what means): {The believers are only those who, when Allah is mentioned, their hearts become fearful, and when His verses are recited to them, it increases them in faith; and upon their Lord they rely.  The ones who establish prayer, and from what We have provided them, they spend. Those are the believers, truly. For them are degrees (of high position) with their Lord and forgiveness and noble provision.} [Quran 8:2-4]

He also says at the end of this soorah (what means): {But those who have believed and emigrated and fought in the cause of Allah and those who gave shelter and aided - it is they who are the believers, truly. For them is forgiveness and noble provision.} [Quran 8:74]

Allah knows best.