What to do in the times of fitnah

No need to go to caves, that time hasn't reached yet. Religious people need to confront secularists, atheists, and so on and so forth.

Finally and most importantly, we need to stick with scholars, mashaikh, tabligh to remain steadfast on shariah. Although this thing has increased importance in this era of fitnahs but it is not that people in past could stay safe without sticking to ulama and mashaikh.

Allah سبحانه وتعالى says in surah kahf:

وَاصْبِرْ نَفْسَكَ مَعَ الَّذِينَ يَدْعُونَ رَبَّهُم بِالْغَدَاةِ وَالْعَشِيِّ يُرِيدُونَ وَجْهَهُ ۖ وَلَا تَعْدُ عَيْنَاكَ عَنْهُمْ تُرِيدُ زِينَةَ الْحَيَاةِ الدُّنْيَا ۖ وَلَا تُطِعْ مَنْ أَغْفَلْنَا قَلْبَهُ عَن ذِكْرِنَا وَاتَّبَعَ هَوَاهُ وَكَانَ أَمْرُهُ فُرُطًا

And keep yourself patient [by being] with those who call upon their Lord in the morning and the evening, seeking His countenance. And let not your eyes pass beyond them, desiring adornments of the worldly life, and do not obey one whose heart We have made heedless of Our remembrance and who follows his desire and whose affair is ever [in] neglect.

Rasoolullah says (Bukhari):

‏إنما مثل الجليس الصالح وجليس السوء، كحامل المسك، ونافخ الكير، فحامل المسك، إما أن يحذيك، وإما أن تبتاع منه، وإما أن تجد منه ريحًا طيبة، ونافخ الكير، إما أن يحرق ثيابك ، وإما أن تجد منه ريحًا منتنة‏

The similitude of good company and that of bad company is that of the owner of musk and of the one blowing the bellows. The owner of musk would either offer you some free of charge, or you would buy it from him, or you smell its pleasant fragrance; and as for the one who blows the bellows (i.e., the blacksmith), he either burns your clothes or you smell a repugnant smell.

Tableegh will NEVER end until the day of Judgement.

Tableeghi Jamaat: This is a METHOD! This is the Ijtehaad of Ulama on doing Tableegh amongst Muslims (in our times) and I agree with you that it will change across countries. Methodology and tactics of work in Pakistan vs England or America will change with time (due to circumstances).

Dajjal: Even when Dajjal shows up you still won't be able to ignore your family and taking care of them so the question doesn't even arise now.

You need to manage things best as you can when Dajjal is here and even now.