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.

I read somewhere that it is an offense to preach the glories of the holy name of the Lord to the faithless. Then what is the way to get the faithless to chant?

There are scriptures. The same scriptures also state that one should follow the words of the Guru without any doubts or questions and act accordingly. Going by that rule, all our masters starting from Chaitanya Mahaprabhu are crying aloud to make the people chant the Holy Name to have them liberated! So we take that path.
Every rule has an exception too!

What is the experience connected with chanting Mantras? When does one get mantra siddhi?

Each Mantra has its own Siddhi. One is said to attain Mantra Siddhi when he is able to see the deity pertaining to his Mantra, by incessant chanting of the Mantra.

Although I have been initiated into the Mahamantra, is it okay if I also chant other Divine Names sometimes like Rama Nama or Arunachala Siva? Or should I chant only the Mahamantra?

The Mantra initiated by the Guru contains a special power. That is the reason why it is recommended that one chant it incessantly. That being said, there is absolutely nothing wrong in chanting any Divine Name of God.

Is chanting while doing work considered as meaningful chanting ? Since most of the days , I am continuously doing house chores one after the other, I don’t get time to sit and do ‘Japa’. But if we chant while doing house chores, does it have same effect ?

Yes. It is definitely great. The Gopis did exactly that way.

Sometimes I start chanting or writing the Mantras without taking bath. Is this allowed? How do I quit this habit?

If you are chanting the Mahamantra, it is harmless. You are not allowed to chant the other Mantras without taking bath. Instead of changing your bathing habit, change over to the Mahamantra. That will prove good for you.

From whom can one take initiation? Is initiation taken only after marriage?

Initiation should be taken from someone who has attained siddhi in that particular mantra. There is no relationship between initiation and marriage.

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.