What's the procedure after giving SAT and TOEFL for B.Tech (lateral entry) abroad in US universities for mechanical polytechnic students?

Yes, TOEFL iBT Home Edition is widely accepted. But this is not accepted by some of the top universities in Europe and some other popular destinations. Make sure to check with universities you are applying.

Over 13,000 institutions globally recognize the TOEFL test for admissions. This includes 100% of all universities in the USA.

No, you won't be eligible for an admission at FU Berlin if you do not get the minimum English Proficiency scores. The English Proficiency tests taken n consideration by Free University of Berlin are –

IELTS: 4.0-7.0

 TOEFL iBT: 95

 PTE (A): 76

C1 Advanced: 180

Yes Shiksha TOEFL online coaching is free in India is trustworthy. They have certified trainers and many students are taking the classes and getting good results. 

You just have to join the free TOEFL classes by Shiksha Study Abroad. They have expert trainers and proven results. There are more than 2000 students took the free TOEFL classes and got a good result.