I am unable to carry out my regular religious ablutions at proper times, owing to my circumstances, as well as my laziness. Will it have any effect if I do not do it in proper time? Can Gayatri Mantra be recited without performance of Sandhya Vandanam?

Whatever you do will certainly have their effects. Unless you are a Gayatri-upasak, you should not chant the Gayatri Mantra as and when you wish. You can chant it as many times as you wish with proper purity, and following the appropriate guidelines prescribed for it in our Scriptures.

Can we chant mantras like ‘Om Namo Narayana’ etc. in the place of Maha Mantra? What impact does it make on our spiritual life?

You can chant any Divine Name of the Lord.
Each Mantra has its own merits and demerits The Maha Mantra has been prescribed in the Shastras as t he means of liberation in this Yuga.
When you chant a mantra, it reverberates with the cosmic and energizes it.
Many Mahans and saints including Sri Chaitanya Maha Prabhu and all his devotees have chanted the Maha Mantra and are still chanting it till date, all over the world. Hence the cosmic is filled with the power of this Name. Thus, by chanting this Mantra, one gets to see the results very soon.
In addition to being a Mantra, this is also a Nama. So, there are absolutely no restrictions to chant this Nama.
That is why Maha Mantra is advocated for liberation.

What is the effect of writing ‘Ram Naam’?Is desire fulfilled if I write ‘Ram Naam’ ?

Absolutely! Why harbour any doubt regarding that?

Is both meditation upon self and chanting the name of Krishna/Rama or Ganesha produce the same effect?

Chanting continuously in the mind, without a gap of even a microsecond – that is meditation.

Amongst all the Names of God which is the greatest? Different people give different Namas.

Any Divine Nama is precious. According to Kali Santarana Upanishad, the ‘Hare Rama..’ Mahamantra is capable of giving deliverance in this Kali Yuga.

When I chant any Mantra, some thoughts run in the back of my mind simultaneously. The moment I realize this happening, the thoughts cease and Japa seems to resume. Now, who is chanting the Mantra and who gets the thoughts? Are both one and the same person?

When the force of air is mild, we call it breeze. When it blows with great force, we call it a storm. In the same way, when the mind imagines, it is called ‘manas’. When it thinks, it is called ‘intellect’.
It is the same person who chants the Mantra as well as gets those thoughts. The phenomenon that you experience is because of the fact that the mind operates at different levels.
It is also the same reason why people perform acts like ‘ashtavadanam’ (performing eight non-connected activities at the same time) etc.

Sri Swamiji initiated me into a Mantra. Which one should I chant? That Mantra or the Maha Mantra?

Chant both.

I have heard that it is necessary to have a Guru initiate one into the Mantra, without which chanting of any mantra is futile. How true is it?

For any mantra, a Guru is a must. For Rama Nama and the Mahamantra, you can start chanting even without a Guru. When you are accepted by a Guru, you can take formal initiation from him and continue. For all other mantras, one can recite it only after proper initiation.

I am writing ‘Ram Nam’ and it has solved many problems of mine and fulfilled many desires. But one crucial desire of mine alone is not getting fulfilled. Why is this happening?

That may be because Lord Rama feels that if this particular desire of yours gets fulfilled, it may create problems in the future. With a human mind, it is impossible to know what would happen in future, but one thing, you can be certain: Lord Rama is always right.

What are the do’s and don’ts to perform Japa of the mantra given by the Guru? Can it be chanted all times, irrespective of the location and dress code (i.e. in office attire wearing shoes etc.)?

The “Rama” Nama and Mahamantra have no rules. You can chant it any number of times, any place, any time of the day and in any state.
Other mantras may have their own restrictions and have to be chanted as instructed by the Guru.