as to best screen recorder I recommend Joyoshare VidiKit, which allows you record your screen, specific web, audio, webcam and gameplay, with no lag and high quality, what's more, it uses easily, friendly for new beginners！

Considering your situation there are several methods you can take to activate your iPhone
1. use screen passcode to unlock your iPhone, you can tap the "Unlock with Passcode"/ "Activation Lock Help" message on the activation lock screen, and select the "Use Device Passcode" option on the pop-up. Then, enter the screen passcode of your iPhone.
2. you can go to iforgot.apple.com to find your Apple ID and passcode back
However, if the above methods cannot solve your issue there still a powerful method can help you: Joyoshare Activation Unlocker, which can activate your iPhone without password and Apple ID

Hey, I think you can download Joyoshare VidiKit to have a try, free download, it can record in 4K and without delay, I used it to record my gamepay, uses pretty good!

I must introduce Joyoshare VidiKit to you ! I used it for a few days and I'm amazed by its rich set of functions absolutely audio record included, I used it to record the video sound for work, it has no time limit which helps me a lot, because some software only can record 3 or 5 minutes, so I must divide my audio into several parts, but now, with Joyoshare Vidikit , I can record all my works in just one file which is much more convenient ! you can download it free on https://www.joyoshare.com/vidikit/

I must recommend Joyoshare VidiKit to you! I have used this software for a long time, it is totally satisfied your needs! it can record your screen just need 1 click and, you can chose whether to record yours and the system voice or not, what I usually do is use it to record my game play , you know, there is no delay during the record! awesome experience!