How can we cultivate the love, devotion and care towards the supreme God? Sri Sri Swamiji mentioned that we should chant the Maha Mantra with devotion and love. So how can we cultivate this love and devotion inside ourselves?

The easiest way to cultivate this devotion and love is through the association of Sadhus and Mahans.

Is it true that even a Bhakta has to go through ‘Vichara’ in order to realize the Self?

No! Not at all!

In Bhagavatam, I remember reading that Bhakti is more difficult to attain than Mukti. Is your preaching (Nama Sankirtan) aiming at Bhakti or Mukti? If what Bhagavatam says is true, any other way to attain the Lord (other than bhakti) must be easier, isn’t it?

Bhakti can be divided into two types – Sadhana Bhakti and Sadhya Bhakti. Sadhya Bhakti is also known as Prema Bhakti. The goal of Sadhana bhakti is Sadhya bhakti, similar to the one of the Gopis. It is that Bhakti that Srimad Bhagavatam refers to as the most difficult, because, the state of Prema Bhakti is nothing but Mukti.
Sadhana bhakti is the nine types of Sadhanas that Prahlada says – Sravanam, Kirtanam, Smaranam, Pada Sevanam, Vandanam, Dasyam, Archanam, Sakhyam and Aatma Nivedanam. When these are done not expecting any worldly return, with the sole aim of attaining Prema Bhakti, it will take us to that state.
Generally, the term ‘Bhakti’ refers to Sadhana Bhakti – the path towards the goal. As a simple example, when we are in the process of making tea, we simply say that “the tea is being made” though tea is not done until the process is over. The same way, the term ‘Bhakti’ is generally used to denote the Sadhana bhakti. But, that is not what Srimad Bhagavatam refers to.