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Yes, you can definitely do BTech course with 50% marks in PCM subjects, as many colleges accept 45%–50% PCM marks for admission. 
Some colleges even give direct admission or admission through entrance exams like JEE, CUET, etc. Given below are some of the top BTech colleges in India accepting admission on 50% marks with their tuition fees and placement package -

Source: The above information has been taken from the official site and may vary.

In short, if you want a BTech degree where food and lodging are included in a budget, it is best to look for a Government-Aided or State University campus.
• Government-Aided Colleges such as CET, JNTUA, TCE subsidizes the tuition and hostel rent, so your total costs over a 4-year period will probably be well within or even below your 8 Lacs budget limit.
• Private Universities such as Kalasalingam or SIMTS have tuition that fits your budget, but hostel and food are considered “services” and are expensive. If you want to keep your costs to 8 lakhs, you will need to opt for the cheapest rooms available, typically non-AC, multi-sharing rooms, and skip all optional campus facilities.

Permanent Residency (called Indefinite Leave to Remain or ILR) in the UK generally requires 5 years of continuous lawful residence. Here is a typical pathway-

Year 1–2- Study (Student Visa).

Year 3–4- Work on Graduate Route Visa (2 years).

Year 5- Switch to Skilled Worker Visa and complete 5 years total to apply for ILR.

Then citizenship- After 1 year of ILR, you can apply for British citizenship.

This 5-year pathway is achievable but requires securing a qualifying job offer within 2 years of graduation on the Graduate Route.

Note- ILR requirements and thresholds are subject to change. Consult an immigration lawyer for personalised advice on your pathway to PR.

Yes Germany offer good ways to permanent residency for international graduates-

•After graduation- You get 18 month Job Seeker Visa to find employment in Germany

•     After finding a job: Apply for a Blue Card (EU Blue Card) if your salary meets the threshold (approx. €43,800/year for most fields; €39,682 for shortage occupations)

•     PR through Blue Card: After 21 months of Blue Card employment (or 33 months normally), you can apply for a Settlement Permit (Niederlassungserlaubnis)

•     Language requirement for PR: B1 level German language proficiency

•     PR is easier to achieve in Germany compared to countries like Australia, Canada, or the UK

Germany actively needs skilled workers — the shortage is especially high in IT, Engineering, Healthcare, and Logistics