  Here is the Python code that performs the tasks you described using the moviepy library:
```
import moviepy.editor as mpy
import subprocess

# Check if required video files exist in current directory
if not mpy.VideoFileClip("video.mp4").is_open():
    # Download video files using youtube-dl command-line tool
    subprocess.run(["youtube-dl", "https://www.youtube.com/watch?v=video_id"])

# Load audio file and extract subclip
audio = mpy.AudioFileClip("audio.mp3")
audio_subclip = audio.subclip(0, 10)

# Apply fade-in and fade-out effects to audio subclip
audio_subclip = audio_subclip.fx(audio_fadein, 10)
audio_subclip = audio_subclip.fx(audio_fadeout, 10)

# Analyze audio subclip to find its period
period = find_video_period(audio_subclip)

# Load video file and extract subclip
video = mpy.VideoFileClip("video.mp4")
video_subclip = video.subclip(0, 10)

# Crop video subclip
video_subclip = video_subclip.crop(0, 0, 10, 10)

# Analyze video subclip to find a segment that loops well
loop_segment = find_loop_segment(video_subclip)

# Extract looping segment from video subclip
loop_video = video_subclip.subclip(loop_segment[0], loop_segment[1])

# Slow down looping video to match audio tempo
loop_video = loop_video.speedx(period / 10)

# Make looping video loop for duration of audio
loop_video = loop_video.loop(period)

# Create mirrored version of looping video
mirrored_loop_video = loop_video.fx(mpy.video.fx.mirror_x)

# Combine original and mirrored video segments side by side
combined_video = mpy.CompositeVideoClip([video_subclip, mirrored_loop_video])

# Apply fade-in and fade-out effects to combined video
combined_video = combined_video.fx(audio_fadein, 10)
combined_video = combined_video.fx(audio_fadeout, 10)

# Add audio to combined video
combined_video = combined_video.set_audio(audio_subclip)

# Create title screen with text overlay
title_screen = mpy.TextClip("Title Screen", font="Arial", fontsize=50, color="white")

# Create credits screen with text on black background
credits_screen = mpy.TextClip("Credits", font="Arial", fontsize=50, color="white", bg_color="black")

# Concatenate title screen, video, and credits screen
concatenated_video = mpy.concatenate_videoclips([title_screen, combined_video, credits_screen])

# Write final video to file
concatenated_video.to_file("output.mp4", fps=30, audio_bitrate=128, bitrate=1000)
```
Note that this code assumes that the required video files are named "video.mp4" and "audio.mp3" and are located in the current directory. You may need to modify the file names and paths to match your specific use case.